{smcl}
{com}{sf}{ul off}{txt}{.-}
      name:  {res}<unnamed>
       {txt}log:  {res}\\isad.isadroot.ex.ac.uk\uoe\user\Submitted New Keynesian Model with Overtime Labor\Referee reports RESTAT\reports 2nd round\Files for RESTAT\NKPC_gmm.smcl
  {txt}log type:  {res}smcl
 {txt}opened on:  {res}19 May 2012, 11:50:43
{txt}
{com}. 
. ivregress gmm  pi_hat ( RULC pi_hat_F1= pi_hat_1  pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 RULC_3 RULC_4 pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2  pi_pc_3 pi_pc_4 longshort_spread_1 longshort_spread_2 longshort_spread_3 longshort_spread_4 logy_detrended_1 logy_detrended_2 logy_detrended_3 logy_detrended_4) in 123/238, noconstant wmatrix(hac nwest optimal)
{res}
{txt}{col 1}Instrumental variables (GMM) regression{col 56}Number of obs{col 70}= {res}    116
{txt}{col 1}{col 56}Wald chi2({res}2{txt}){col 70}={res}       .
{txt}{col 1}{col 56}Prob > chi2{col 70}= {res}      .
{txt}{col 1}{col 56}R-squared{col 70}={res}       .
{txt}{col 1}GMM weight matrix: HAC Bartlett 7     {col 56}Root MSE{col 70}= {res}  .0102

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 14}{c |}{col 26}      HAC
{col 1}      pi_hat{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      z{col 46}   P>|z|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 8}RULC {c |}{col 14}{res}{space 2} .0365158{col 26}{space 2}  .019116{col 37}{space 1}    1.91{col 46}{space 3}0.056{col 54}{space 4}-.0009509{col 67}{space 3} .0739825
{txt}{space 3}pi_hat_F1 {c |}{col 14}{res}{space 2}  .958203{col 26}{space 2} .0237252{col 37}{space 1}   40.39{col 46}{space 3}0.000{col 54}{space 4} .9117024{col 67}{space 3} 1.004704
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{p 0 15 22}Instrumented:{space 2}RULC pi_hat_F1{p_end}
{p 0 15 22}Instruments:{space 3}pi_hat_1 pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 RULC_3 RULC_4 pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2 pi_pc_3 pi_pc_4 longshort_spread_1 longshort_spread_2 longshort_spread_3 longshort_spread_4 logy_detrended_1 logy_detrended_2 logy_detrended_3 logy_detrended_4{p_end}
HAC VCE:{col 16}Bartlett kernel with 10 lags
HAC Lags:{col 16}Chosen by Newey-West method
WMat Lags:{col 16}Chosen by Newey-West method

{com}. 
. estat overid

{txt}{col 3}Test of overidentifying restriction:

{col 3}Hansen's J chi2({res}22{txt}) ={res}  10.642{txt} (p = {res}0.9795{txt})

{com}. 
. matrix list e(V)
{res}
{txt}symmetric e(V)[2,2]
                 RULC   pi_hat_F1
     RULC {res}  .00036542
{txt}pi_hat_F1 {res} -.00027775   .00056289
{reset}
{com}. 
. //notice that the bandwidth of Newey-West's kernel is equal to the number of lags+1
. 
. ivreg2  pi_hat ( RULC pi_hat_F1= pi_hat_1  pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 RULC_3 RULC_4 pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2  pi_pc_3 pi_pc_4 longshort_spread_1 longshort_spread_2 longshort_spread_3 longshort_spread_4 logy_detrended_1 logy_detrended_2 logy_detrended_3 logy_detrended_4) in 123/238, noconstant robust gmm2s nofooter bw(8) first ffirst
{res}
{txt}First-stage regressions
{hline 23}

First-stage regression of RULC:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=8
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 24,    92) = {res}  168.09
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0502750189{txt}{col 55}Centered R2   = {res}  0.8956
{txt}Total (uncentered) SS   = {res}  .053911445{txt}{col 55}Uncentered R2 = {res}  0.9026
{txt}Residual SS             = {res} .0052493242{txt}{col 55}Root MSE      = {res} .007554

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}              RULC{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_1 {c |}{col 20}{res}{space 2} .0498459{col 32}{space 2} .1009364{col 43}{space 1}    0.49{col 52}{space 3}0.623{col 60}{space 4}-.1506226{col 73}{space 3} .2503144
{txt}{space 10}pi_hat_2 {c |}{col 20}{res}{space 2}-.1928227{col 32}{space 2} .1491651{col 43}{space 1}   -1.29{col 52}{space 3}0.199{col 60}{space 4}-.4890774{col 73}{space 3} .1034321
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2}-.0051205{col 32}{space 2} .0881314{col 43}{space 1}   -0.06{col 52}{space 3}0.954{col 60}{space 4} -.180157{col 73}{space 3}  .169916
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2} .2357714{col 32}{space 2} .1244063{col 43}{space 1}    1.90{col 52}{space 3}0.061{col 60}{space 4}-.0113102{col 73}{space 3}  .482853
{txt}{space 12}RULC_1 {c |}{col 20}{res}{space 2} .6893057{col 32}{space 2}  .119659{col 43}{space 1}    5.76{col 52}{space 3}0.000{col 60}{space 4} .4516526{col 73}{space 3} .9269588
{txt}{space 12}RULC_2 {c |}{col 20}{res}{space 2} .0866058{col 32}{space 2} .1736684{col 43}{space 1}    0.50{col 52}{space 3}0.619{col 60}{space 4}-.2583145{col 73}{space 3} .4315262
{txt}{space 12}RULC_3 {c |}{col 20}{res}{space 2} .3493403{col 32}{space 2} .1905658{col 43}{space 1}    1.83{col 52}{space 3}0.070{col 60}{space 4}-.0291398{col 73}{space 3} .7278204
{txt}{space 12}RULC_4 {c |}{col 20}{res}{space 2}-.2251623{col 32}{space 2} .1463981{col 43}{space 1}   -1.54{col 52}{space 3}0.127{col 60}{space 4}-.5159215{col 73}{space 3} .0655969
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2} .0271108{col 32}{space 2} .0419511{col 43}{space 1}    0.65{col 52}{space 3}0.520{col 60}{space 4}-.0562077{col 73}{space 3} .1104293
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0578956{col 32}{space 2} .0565722{col 43}{space 1}    1.02{col 52}{space 3}0.309{col 60}{space 4}-.0544617{col 73}{space 3} .1702528
{txt}{space 12}pi_w_3 {c |}{col 20}{res}{space 2} -.091333{col 32}{space 2} .0331411{col 43}{space 1}   -2.76{col 52}{space 3}0.007{col 60}{space 4} -.157154{col 73}{space 3} -.025512
{txt}{space 12}pi_w_4 {c |}{col 20}{res}{space 2}  .070176{col 32}{space 2} .0293728{col 43}{space 1}    2.39{col 52}{space 3}0.019{col 60}{space 4} .0118391{col 73}{space 3} .1285129
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2} -.008986{col 32}{space 2}  .044154{col 43}{space 1}   -0.20{col 52}{space 3}0.839{col 60}{space 4}-.0966795{col 73}{space 3} .0787076
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .0346486{col 32}{space 2} .0459027{col 43}{space 1}    0.75{col 52}{space 3}0.452{col 60}{space 4}-.0565181{col 73}{space 3} .1258153
{txt}{space 11}pi_pc_3 {c |}{col 20}{res}{space 2}-.0238936{col 32}{space 2} .0355371{col 43}{space 1}   -0.67{col 52}{space 3}0.503{col 60}{space 4}-.0944734{col 73}{space 3} .0466861
{txt}{space 11}pi_pc_4 {c |}{col 20}{res}{space 2}-.0018019{col 32}{space 2} .0289653{col 43}{space 1}   -0.06{col 52}{space 3}0.951{col 60}{space 4}-.0593295{col 73}{space 3} .0557257
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2} .0029785{col 32}{space 2} .0023779{col 43}{space 1}    1.25{col 52}{space 3}0.214{col 60}{space 4}-.0017442{col 73}{space 3} .0077011
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2}-.0049786{col 32}{space 2} .0025611{col 43}{space 1}   -1.94{col 52}{space 3}0.055{col 60}{space 4}-.0100652{col 73}{space 3}  .000108
{txt}longshort_spread_3 {c |}{col 20}{res}{space 2}   .00228{col 32}{space 2}  .002087{col 43}{space 1}    1.09{col 52}{space 3}0.277{col 60}{space 4}-.0018651{col 73}{space 3}  .006425
{txt}longshort_spread_4 {c |}{col 20}{res}{space 2}-.0010922{col 32}{space 2} .0021427{col 43}{space 1}   -0.51{col 52}{space 3}0.611{col 60}{space 4}-.0053477{col 73}{space 3} .0031634
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2} .0324061{col 32}{space 2}  .194215{col 43}{space 1}    0.17{col 52}{space 3}0.868{col 60}{space 4}-.3533216{col 73}{space 3} .4181339
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2}-.0556258{col 32}{space 2} .2668791{col 43}{space 1}   -0.21{col 52}{space 3}0.835{col 60}{space 4}-.5856707{col 73}{space 3} .4744192
{txt}{space 2}logy_detrended_3 {c |}{col 20}{res}{space 2} .5213236{col 32}{space 2} .1598489{col 43}{space 1}    3.26{col 52}{space 3}0.002{col 60}{space 4} .2038498{col 73}{space 3} .8387974
{txt}{space 2}logy_detrended_4 {c |}{col 20}{res}{space 2}-.4155764{col 32}{space 2} .1487731{col 43}{space 1}   -2.79{col 52}{space 3}0.006{col 60}{space 4}-.7110526{col 73}{space 3}-.1201003
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_1 pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 RULC_3
{col 23}RULC_4 pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2 pi_pc_3
{col 23}pi_pc_4 longshort_spread_1 longshort_spread_2
{col 23}longshort_spread_3 longshort_spread_4 logy_detrended_1
{col 23}logy_detrended_2 logy_detrended_3 logy_detrended_4
{hline 78}
F test of excluded instruments:
  F( 24,    92) = {res}  168.09
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 23,    92) = {res}   58.24
{txt}  Prob > F      = {res}  0.0000

{txt}First-stage regression of pi_hat_F1:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=8
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 24,    92) = {res}   65.36
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0579688024{txt}{col 55}Centered R2   = {res}  0.8656
{txt}Total (uncentered) SS   = {res} .0582406245{txt}{col 55}Uncentered R2 = {res}  0.8663
{txt}Residual SS             = {res} .0077892498{txt}{col 55}Root MSE      = {res} .009201

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}         pi_hat_F1{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_1 {c |}{col 20}{res}{space 2} .3745063{col 32}{space 2} .0887286{col 43}{space 1}    4.22{col 52}{space 3}0.000{col 60}{space 4} .1982837{col 73}{space 3} .5507289
{txt}{space 10}pi_hat_2 {c |}{col 20}{res}{space 2} .1325837{col 32}{space 2} .1307324{col 43}{space 1}    1.01{col 52}{space 3}0.313{col 60}{space 4} -.127062{col 73}{space 3} .3922295
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2} .3143254{col 32}{space 2} .1056396{col 43}{space 1}    2.98{col 52}{space 3}0.004{col 60}{space 4} .1045161{col 73}{space 3} .5241348
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2}  .009684{col 32}{space 2} .0918234{col 43}{space 1}    0.11{col 52}{space 3}0.916{col 60}{space 4}-.1726852{col 73}{space 3} .1920533
{txt}{space 12}RULC_1 {c |}{col 20}{res}{space 2} .1067482{col 32}{space 2} .1697428{col 43}{space 1}    0.63{col 52}{space 3}0.531{col 60}{space 4}-.2303756{col 73}{space 3} .4438721
{txt}{space 12}RULC_2 {c |}{col 20}{res}{space 2}-.5516888{col 32}{space 2} .1823908{col 43}{space 1}   -3.02{col 52}{space 3}0.003{col 60}{space 4}-.9139326{col 73}{space 3} -.189445
{txt}{space 12}RULC_3 {c |}{col 20}{res}{space 2} .3485626{col 32}{space 2} .2635635{col 43}{space 1}    1.32{col 52}{space 3}0.189{col 60}{space 4}-.1748974{col 73}{space 3} .8720225
{txt}{space 12}RULC_4 {c |}{col 20}{res}{space 2} .1125691{col 32}{space 2} .1549352{col 43}{space 1}    0.73{col 52}{space 3}0.469{col 60}{space 4}-.1951456{col 73}{space 3} .4202838
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2} .0532054{col 32}{space 2} .0439785{col 43}{space 1}    1.21{col 52}{space 3}0.229{col 60}{space 4}-.0341397{col 73}{space 3} .1405504
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0972882{col 32}{space 2} .0458506{col 43}{space 1}    2.12{col 52}{space 3}0.037{col 60}{space 4}  .006225{col 73}{space 3} .1883515
{txt}{space 12}pi_w_3 {c |}{col 20}{res}{space 2} .0183833{col 32}{space 2} .0421642{col 43}{space 1}    0.44{col 52}{space 3}0.664{col 60}{space 4}-.0653584{col 73}{space 3}  .102125
{txt}{space 12}pi_w_4 {c |}{col 20}{res}{space 2}-.0004034{col 32}{space 2} .0333421{col 43}{space 1}   -0.01{col 52}{space 3}0.990{col 60}{space 4}-.0666237{col 73}{space 3} .0658169
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2} .0661874{col 32}{space 2} .0475622{col 43}{space 1}    1.39{col 52}{space 3}0.167{col 60}{space 4}-.0282751{col 73}{space 3}   .16065
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .1084292{col 32}{space 2} .0611923{col 43}{space 1}    1.77{col 52}{space 3}0.080{col 60}{space 4}-.0131039{col 73}{space 3} .2299624
{txt}{space 11}pi_pc_3 {c |}{col 20}{res}{space 2}  .039158{col 32}{space 2}  .036866{col 43}{space 1}    1.06{col 52}{space 3}0.291{col 60}{space 4} -.034061{col 73}{space 3}  .112377
{txt}{space 11}pi_pc_4 {c |}{col 20}{res}{space 2}-.0343521{col 32}{space 2} .0361454{col 43}{space 1}   -0.95{col 52}{space 3}0.344{col 60}{space 4}-.1061399{col 73}{space 3} .0374357
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2} .0014412{col 32}{space 2}  .003373{col 43}{space 1}    0.43{col 52}{space 3}0.670{col 60}{space 4}-.0052578{col 73}{space 3} .0081402
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2} .0010073{col 32}{space 2} .0025903{col 43}{space 1}    0.39{col 52}{space 3}0.698{col 60}{space 4}-.0041372{col 73}{space 3} .0061518
{txt}longshort_spread_3 {c |}{col 20}{res}{space 2}-.0022456{col 32}{space 2} .0027849{col 43}{space 1}   -0.81{col 52}{space 3}0.422{col 60}{space 4}-.0077766{col 73}{space 3} .0032855
{txt}longshort_spread_4 {c |}{col 20}{res}{space 2} .0028109{col 32}{space 2} .0020064{col 43}{space 1}    1.40{col 52}{space 3}0.165{col 60}{space 4} -.001174{col 73}{space 3} .0067958
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2} .2964851{col 32}{space 2} .2026049{col 43}{space 1}    1.46{col 52}{space 3}0.147{col 60}{space 4}-.1059057{col 73}{space 3}  .698876
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2}-.5541281{col 32}{space 2} .2552916{col 43}{space 1}   -2.17{col 52}{space 3}0.033{col 60}{space 4}-1.061159{col 73}{space 3} -.047097
{txt}{space 2}logy_detrended_3 {c |}{col 20}{res}{space 2}  .543625{col 32}{space 2} .2877449{col 43}{space 1}    1.89{col 52}{space 3}0.062{col 60}{space 4}-.0278613{col 73}{space 3} 1.115111
{txt}{space 2}logy_detrended_4 {c |}{col 20}{res}{space 2}-.1430057{col 32}{space 2} .1593738{col 43}{space 1}   -0.90{col 52}{space 3}0.372{col 60}{space 4}-.4595359{col 73}{space 3} .1735245
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_1 pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 RULC_3
{col 23}RULC_4 pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2 pi_pc_3
{col 23}pi_pc_4 longshort_spread_1 longshort_spread_2
{col 23}longshort_spread_3 longshort_spread_4 logy_detrended_1
{col 23}logy_detrended_2 logy_detrended_3 logy_detrended_4
{hline 78}
F test of excluded instruments:
  F( 24,    92) = {res}   65.36
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 23,    92) = {res}   50.83
{txt}  Prob > F      = {res}  0.0000



{txt}Summary results for first-stage regressions
{hline 43}

{col 44}{help ivreg2##apstats:(Underid)}{col 65}{help ivreg2##apstats:(Weak id)}
Variable     |{col 16}{help ivreg2##apstats:F}({res}{col 17} 24{txt},{res}    92{txt})  P-val{col 37}|{col 39}{help ivreg2##apstats:AP Chi-sq}({res} 23{txt}) P-val{col 60}|{col 62}{help ivreg2##apstats:AP F}({res}{col 67} 23{txt},{res}    92{txt})
{res}RULC        {col 14}{txt}|{col 18}{res}  168.09{col 28}  0.0000{col 37}{txt}|{col 42}{res} 1688.88{col 51}  0.0000{col 60}{txt}|{col 65}{res}   58.24
pi_hat_F1   {col 14}{txt}|{col 18}{res}   65.36{col 28}  0.0000{col 37}{txt}|{col 42}{res} 1474.10{col 51}  0.0000{col 60}{txt}|{col 65}{res}   50.83

{txt}NB: first-stage test statistics heteroskedasticity and autocorrelation-robust

Stock-Yogo weak ID test critical values for single endogenous regressor:
{res}{txt}{col 37}5% maximal IV relative bias{res}{col 67} 21.41
{txt}{col 36}10% maximal IV relative bias{res}{col 67} 11.41
{txt}{col 36}20% maximal IV relative bias{res}{col 67}  6.22
{txt}{col 36}30% maximal IV relative bias{res}{col 67}  4.41
{txt}{col 36}10% maximal IV size{res}{col 67} 69.46
{txt}{col 36}15% maximal IV size{res}{col 67} 36.37
{txt}{col 36}20% maximal IV size{res}{col 67} 25.10
{txt}{col 36}25% maximal IV size{res}{col 67} 19.41
{txt}Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

{help ivreg2##idtest:Underidentification test}
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
{res}Kleibergen-Paap rk LM statistic{txt}{col 42}Chi-sq({res}23{txt})={res}10.89  {col 61}{txt}P-val={res}0.9843

{help ivreg2##widtest:Weak identification test}
{txt}Ho: equation is weakly identified
{res}Cragg-Donald Wald F statistic{col 65}   13.37
Kleibergen-Paap Wald rk F statistic{col 65}   50.21

{txt}Stock-Yogo weak ID test critical values for K1=2 and L1=24:
{res}{txt}{col 37}5% maximal IV relative bias{res}{col 67} 20.69
{txt}{col 36}10% maximal IV relative bias{res}{col 67} 11.05
{txt}{col 36}20% maximal IV relative bias{res}{col 67}  6.06
{txt}{col 36}30% maximal IV relative bias{res}{col 67}  4.32
{txt}{col 36}10% maximal IV size{res}{col 67} 53.39
{txt}{col 36}15% maximal IV size{res}{col 67} 28.42
{txt}{col 36}20% maximal IV size{res}{col 67} 19.97
{txt}{col 36}25% maximal IV size{res}{col 67} 15.64
{txt}Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

{help ivreg2##wirobust:Weak-instrument-robust inference}
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
{res}Anderson-Rubin Wald test{txt}{col 36}F({res}24{txt},{res}92{txt})={col 49}{res} 120.79{col 61}{txt}P-val={res}0.0000
Anderson-Rubin Wald test{txt}{col 36}Chi-sq({res}24{txt})={col 49}{res}3655.15{col 61}{txt}P-val={res}0.0000
Stock-Wright LM S statistic{txt}{col 36}Chi-sq({res}24{txt})={col 49}{res}  10.97{col 61}{txt}P-val={res}0.9893

{txt}NB: Underidentification, weak identification and weak-identification-robust
    test statistics heteroskedasticity and autocorrelation-robust

Number of observations               N  = {res}       116
{txt}Number of regressors                 K  = {res}         2
{txt}Number of endogenous regressors      K1 = {res}         2
{txt}Number of instruments                L  = {res}        24
{txt}Number of excluded instruments       L1 = {res}        24

{txt}2-Step GMM estimation
{hline 21}

Estimates efficient for arbitrary heteroskedasticity and autocorrelation
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=8
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F(  2,   114) = {res} 1819.69
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0581346117{txt}{col 55}Centered R2   = {res}  0.7924
{txt}Total (uncentered) SS   = {res} .0584658598{txt}{col 55}Uncentered R2 = {res}  0.7936
{txt}Residual SS             = {res} .0120675155{txt}{col 55}Root MSE      = {res}   .0102

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 14}{c |}{col 26}    Robust
{col 1}      pi_hat{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      z{col 46}   P>|z|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 8}RULC {c |}{col 14}{res}{space 2} .0365158{col 26}{space 2} .0211183{col 37}{space 1}    1.73{col 46}{space 3}0.084{col 54}{space 4}-.0048753{col 67}{space 3}  .077907
{txt}{space 3}pi_hat_F1 {c |}{col 14}{res}{space 2}  .958203{col 26}{space 2} .0208306{col 37}{space 1}   46.00{col 46}{space 3}0.000{col 54}{space 4} .9173759{col 67}{space 3} .9990302
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. 
. ivregress gmm  pi_hat ( RULC pi_hat_F1= pi_hat_1  pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 pi_w_1 pi_w_2 pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2 logy_detrended_1 logy_detrended_2) in 123/238, noconstant wmatrix(hac nwest optimal)
{res}
{txt}{col 1}Instrumental variables (GMM) regression{col 56}Number of obs{col 70}= {res}    116
{txt}{col 1}{col 56}Wald chi2({res}2{txt}){col 70}={res}       .
{txt}{col 1}{col 56}Prob > chi2{col 70}= {res}      .
{txt}{col 1}{col 56}R-squared{col 70}={res}       .
{txt}{col 1}GMM weight matrix: HAC Bartlett 8     {col 56}Root MSE{col 70}= {res} .01024

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 14}{c |}{col 26}      HAC
{col 1}      pi_hat{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      z{col 46}   P>|z|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 8}RULC {c |}{col 14}{res}{space 2} .0389173{col 26}{space 2} .0494061{col 37}{space 1}    0.79{col 46}{space 3}0.431{col 54}{space 4} -.057917{col 67}{space 3} .1357515
{txt}{space 3}pi_hat_F1 {c |}{col 14}{res}{space 2} .9675573{col 26}{space 2} .0606009{col 37}{space 1}   15.97{col 46}{space 3}0.000{col 54}{space 4} .8487816{col 67}{space 3} 1.086333
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{p 0 15 22}Instrumented:{space 2}RULC pi_hat_F1{p_end}
{p 0 15 22}Instruments:{space 3}pi_hat_1 pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 pi_w_1 pi_w_2 pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2 logy_detrended_1 logy_detrended_2{p_end}
HAC VCE:{col 16}Bartlett kernel with 1 lags
HAC Lags:{col 16}Chosen by Newey-West method
WMat Lags:{col 16}Chosen by Newey-West method

{com}. 
. estat overid

{txt}{col 3}Test of overidentifying restriction:

{col 3}Hansen's J chi2({res}12{txt}) ={res} 8.10218{txt} (p = {res}0.7771{txt})

{com}. 
. matrix list e(V)
{res}
{txt}symmetric e(V)[2,2]
                 RULC   pi_hat_F1
     RULC {res}  .00244097
{txt}pi_hat_F1 {res} -.00185705   .00367247
{reset}
{com}. 
. ivreg2  pi_hat ( RULC pi_hat_F1= pi_hat_1  pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 pi_w_1 pi_w_2 pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2 logy_detrended_1 logy_detrended_2) in 123/238, noconstant robust gmm2s nofooter bw(9) first ffirst
{res}
{txt}First-stage regressions
{hline 23}

First-stage regression of RULC:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=9
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 14,   102) = {res}  127.32
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0502750189{txt}{col 55}Centered R2   = {res}  0.8735
{txt}Total (uncentered) SS   = {res}  .053911445{txt}{col 55}Uncentered R2 = {res}  0.8820
{txt}Residual SS             = {res} .0063600651{txt}{col 55}Root MSE      = {res} .007896

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}              RULC{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_1 {c |}{col 20}{res}{space 2} .0484782{col 32}{space 2} .1288536{col 43}{space 1}    0.38{col 52}{space 3}0.708{col 60}{space 4}-.2071023{col 73}{space 3} .3040587
{txt}{space 10}pi_hat_2 {c |}{col 20}{res}{space 2}-.1592347{col 32}{space 2} .1422707{col 43}{space 1}   -1.12{col 52}{space 3}0.266{col 60}{space 4}-.4414281{col 73}{space 3} .1229586
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2}-.0219103{col 32}{space 2} .0696101{col 43}{space 1}   -0.31{col 52}{space 3}0.754{col 60}{space 4}-.1599815{col 73}{space 3}  .116161
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2} .2114014{col 32}{space 2} .1182955{col 43}{space 1}    1.79{col 52}{space 3}0.077{col 60}{space 4}-.0232372{col 73}{space 3}   .44604
{txt}{space 12}RULC_1 {c |}{col 20}{res}{space 2} .7353615{col 32}{space 2} .1358402{col 43}{space 1}    5.41{col 52}{space 3}0.000{col 60}{space 4} .4659231{col 73}{space 3}   1.0048
{txt}{space 12}RULC_2 {c |}{col 20}{res}{space 2} .1594837{col 32}{space 2} .1437936{col 43}{space 1}    1.11{col 52}{space 3}0.270{col 60}{space 4}-.1257302{col 73}{space 3} .4446977
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2}-.0086676{col 32}{space 2} .0373649{col 43}{space 1}   -0.23{col 52}{space 3}0.817{col 60}{space 4}-.0827808{col 73}{space 3} .0654456
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0384582{col 32}{space 2} .0470836{col 43}{space 1}    0.82{col 52}{space 3}0.416{col 60}{space 4}-.0549319{col 73}{space 3} .1318483
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2}-.0499324{col 32}{space 2} .0402718{col 43}{space 1}   -1.24{col 52}{space 3}0.218{col 60}{space 4}-.1298114{col 73}{space 3} .0299466
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .0417603{col 32}{space 2} .0457249{col 43}{space 1}    0.91{col 52}{space 3}0.363{col 60}{space 4}-.0489349{col 73}{space 3} .1324555
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2} .0024332{col 32}{space 2} .0026418{col 43}{space 1}    0.92{col 52}{space 3}0.359{col 60}{space 4}-.0028069{col 73}{space 3} .0076732
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2}-.0033579{col 32}{space 2}  .002464{col 43}{space 1}   -1.36{col 52}{space 3}0.176{col 60}{space 4}-.0082452{col 73}{space 3} .0015295
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2} .1531972{col 32}{space 2} .1263437{col 43}{space 1}    1.21{col 52}{space 3}0.228{col 60}{space 4}-.0974049{col 73}{space 3} .4037993
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2}-.0342508{col 32}{space 2} .1248243{col 43}{space 1}   -0.27{col 52}{space 3}0.784{col 60}{space 4}-.2818391{col 73}{space 3} .2133375
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_1 pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 pi_w_1
{col 23}pi_w_2 pi_pc_1 pi_pc_2 longshort_spread_1
{col 23}longshort_spread_2 logy_detrended_1 logy_detrended_2
{hline 78}
F test of excluded instruments:
  F( 14,   102) = {res}  127.32
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 13,   102) = {res}   60.03
{txt}  Prob > F      = {res}  0.0000

{txt}First-stage regression of pi_hat_F1:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=9
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 14,   102) = {res}   27.32
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0579688024{txt}{col 55}Centered R2   = {res}  0.8500
{txt}Total (uncentered) SS   = {res} .0582406245{txt}{col 55}Uncentered R2 = {res}  0.8507
{txt}Residual SS             = {res} .0086965892{txt}{col 55}Root MSE      = {res} .009234

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}         pi_hat_F1{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_1 {c |}{col 20}{res}{space 2} .3509578{col 32}{space 2} .1039703{col 43}{space 1}    3.38{col 52}{space 3}0.001{col 60}{space 4} .1447333{col 73}{space 3} .5571824
{txt}{space 10}pi_hat_2 {c |}{col 20}{res}{space 2} .2170901{col 32}{space 2} .1000909{col 43}{space 1}    2.17{col 52}{space 3}0.032{col 60}{space 4} .0185604{col 73}{space 3} .4156198
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2} .3813234{col 32}{space 2} .0842209{col 43}{space 1}    4.53{col 52}{space 3}0.000{col 60}{space 4} .2142716{col 73}{space 3} .5483752
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2}-.0477351{col 32}{space 2} .0915848{col 43}{space 1}   -0.52{col 52}{space 3}0.603{col 60}{space 4} -.229393{col 73}{space 3} .1339229
{txt}{space 12}RULC_1 {c |}{col 20}{res}{space 2} .0869067{col 32}{space 2} .1349154{col 43}{space 1}    0.64{col 52}{space 3}0.521{col 60}{space 4}-.1806974{col 73}{space 3} .3545109
{txt}{space 12}RULC_2 {c |}{col 20}{res}{space 2}-.1260085{col 32}{space 2} .1343167{col 43}{space 1}   -0.94{col 52}{space 3}0.350{col 60}{space 4}-.3924249{col 73}{space 3}  .140408
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2} .0452391{col 32}{space 2} .0373412{col 43}{space 1}    1.21{col 52}{space 3}0.229{col 60}{space 4}-.0288269{col 73}{space 3} .1193052
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0300653{col 32}{space 2} .0307892{col 43}{space 1}    0.98{col 52}{space 3}0.331{col 60}{space 4}-.0310049{col 73}{space 3} .0911356
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2} .0450165{col 32}{space 2} .0498326{col 43}{space 1}    0.90{col 52}{space 3}0.368{col 60}{space 4}-.0538262{col 73}{space 3} .1438592
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .0720801{col 32}{space 2} .0654659{col 43}{space 1}    1.10{col 52}{space 3}0.273{col 60}{space 4}-.0577712{col 73}{space 3} .2019314
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2}   .00201{col 32}{space 2} .0034321{col 43}{space 1}    0.59{col 52}{space 3}0.559{col 60}{space 4}-.0047975{col 73}{space 3} .0088175
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2} .0007357{col 32}{space 2}  .002697{col 43}{space 1}    0.27{col 52}{space 3}0.786{col 60}{space 4}-.0046137{col 73}{space 3} .0060852
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2} .1821731{col 32}{space 2} .2008191{col 43}{space 1}    0.91{col 52}{space 3}0.366{col 60}{space 4}-.2161507{col 73}{space 3} .5804969
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2}-.0347379{col 32}{space 2} .1969675{col 43}{space 1}   -0.18{col 52}{space 3}0.860{col 60}{space 4}-.4254219{col 73}{space 3} .3559462
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_1 pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 pi_w_1
{col 23}pi_w_2 pi_pc_1 pi_pc_2 longshort_spread_1
{col 23}longshort_spread_2 logy_detrended_1 logy_detrended_2
{hline 78}
F test of excluded instruments:
  F( 14,   102) = {res}   27.32
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 13,   102) = {res}   22.89
{txt}  Prob > F      = {res}  0.0000



{txt}Summary results for first-stage regressions
{hline 43}

{col 44}{help ivreg2##apstats:(Underid)}{col 65}{help ivreg2##apstats:(Weak id)}
Variable     |{col 16}{help ivreg2##apstats:F}({res}{col 17} 14{txt},{res}   102{txt})  P-val{col 37}|{col 39}{help ivreg2##apstats:AP Chi-sq}({res} 13{txt}) P-val{col 60}|{col 62}{help ivreg2##apstats:AP F}({res}{col 67} 13{txt},{res}   102{txt})
{res}RULC        {col 14}{txt}|{col 18}{res}  127.32{col 28}  0.0000{col 37}{txt}|{col 42}{res}  887.50{col 51}  0.0000{col 60}{txt}|{col 65}{res}   60.03
pi_hat_F1   {col 14}{txt}|{col 18}{res}   27.32{col 28}  0.0000{col 37}{txt}|{col 42}{res}  338.38{col 51}  0.0000{col 60}{txt}|{col 65}{res}   22.89

{txt}NB: first-stage test statistics heteroskedasticity and autocorrelation-robust

Stock-Yogo weak ID test critical values for single endogenous regressor:
{res}{txt}{col 37}5% maximal IV relative bias{res}{col 67} 21.18
{txt}{col 36}10% maximal IV relative bias{res}{col 67} 11.52
{txt}{col 36}20% maximal IV relative bias{res}{col 67}  6.49
{txt}{col 36}30% maximal IV relative bias{res}{col 67}  4.71
{txt}{col 36}10% maximal IV size{res}{col 67} 45.64
{txt}{col 36}15% maximal IV size{res}{col 67} 24.42
{txt}{col 36}20% maximal IV size{res}{col 67} 17.14
{txt}{col 36}25% maximal IV size{res}{col 67} 13.41
{txt}Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

{help ivreg2##idtest:Underidentification test}
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
{res}Kleibergen-Paap rk LM statistic{txt}{col 42}Chi-sq({res}13{txt})={res}8.32   {col 61}{txt}P-val={res}0.8221

{help ivreg2##widtest:Weak identification test}
{txt}Ho: equation is weakly identified
{res}Cragg-Donald Wald F statistic{col 65}   22.67
Kleibergen-Paap Wald rk F statistic{col 65}   60.68

{txt}Stock-Yogo weak ID test critical values for K1=2 and L1=14:
{res}{txt}{col 37}5% maximal IV relative bias{res}{col 67} 19.83
{txt}{col 36}10% maximal IV relative bias{res}{col 67} 10.89
{txt}{col 36}20% maximal IV relative bias{res}{col 67}  6.20
{txt}{col 36}30% maximal IV relative bias{res}{col 67}  4.53
{txt}{col 36}10% maximal IV size{res}{col 67} 36.36
{txt}{col 36}15% maximal IV size{res}{col 67} 19.72
{txt}{col 36}20% maximal IV size{res}{col 67} 14.05
{txt}{col 36}25% maximal IV size{res}{col 67} 11.13
{txt}Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

{help ivreg2##wirobust:Weak-instrument-robust inference}
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
{res}Anderson-Rubin Wald test{txt}{col 36}F({res}14{txt},{res}102{txt})={col 49}{res} 124.62{col 61}{txt}P-val={res}0.0000
Anderson-Rubin Wald test{txt}{col 36}Chi-sq({res}14{txt})={col 49}{res}1984.16{col 61}{txt}P-val={res}0.0000
Stock-Wright LM S statistic{txt}{col 36}Chi-sq({res}14{txt})={col 49}{res}   9.02{col 61}{txt}P-val={res}0.8297

{txt}NB: Underidentification, weak identification and weak-identification-robust
    test statistics heteroskedasticity and autocorrelation-robust

Number of observations               N  = {res}       116
{txt}Number of regressors                 K  = {res}         2
{txt}Number of endogenous regressors      K1 = {res}         2
{txt}Number of instruments                L  = {res}        14
{txt}Number of excluded instruments       L1 = {res}        14

{txt}2-Step GMM estimation
{hline 21}

Estimates efficient for arbitrary heteroskedasticity and autocorrelation
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=9
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F(  2,   114) = {res}  823.67
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0581346117{txt}{col 55}Centered R2   = {res}  0.7908
{txt}Total (uncentered) SS   = {res} .0584658598{txt}{col 55}Uncentered R2 = {res}  0.7920
{txt}Residual SS             = {res} .0121623753{txt}{col 55}Root MSE      = {res}  .01024

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 14}{c |}{col 26}    Robust
{col 1}      pi_hat{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      z{col 46}   P>|z|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 8}RULC {c |}{col 14}{res}{space 2} .0389173{col 26}{space 2} .0300908{col 37}{space 1}    1.29{col 46}{space 3}0.196{col 54}{space 4}-.0200597{col 67}{space 3} .0978942
{txt}{space 3}pi_hat_F1 {c |}{col 14}{res}{space 2} .9675573{col 26}{space 2} .0294835{col 37}{space 1}   32.82{col 46}{space 3}0.000{col 54}{space 4} .9097706{col 67}{space 3} 1.025344
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. 
. ivregress gmm  pi_hat ( ROLC pi_hat_F1= pi_hat_1  pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 ROLC_3 ROLC_4 pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2  pi_pc_3 pi_pc_4 longshort_spread_1 longshort_spread_2 longshort_spread_3 longshort_spread_4 logy_detrended_1 logy_detrended_2 logy_detrended_3 logy_detrended_4) in 123/238, noconstant wmatrix(hac nwest optimal)
{res}
{txt}{col 1}Instrumental variables (GMM) regression{col 56}Number of obs{col 70}= {res}    116
{txt}{col 1}{col 56}Wald chi2({res}2{txt}){col 70}={res}       .
{txt}{col 1}{col 56}Prob > chi2{col 70}= {res}      .
{txt}{col 1}{col 56}R-squared{col 70}={res}       .
{txt}{col 1}GMM weight matrix: HAC Bartlett 9     {col 56}Root MSE{col 70}= {res} .01025

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 14}{c |}{col 26}      HAC
{col 1}      pi_hat{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      z{col 46}   P>|z|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 8}ROLC {c |}{col 14}{res}{space 2}-.0342342{col 26}{space 2} .0146808{col 37}{space 1}   -2.33{col 46}{space 3}0.020{col 54}{space 4}-.0630081{col 67}{space 3}-.0054603
{txt}{space 3}pi_hat_F1 {c |}{col 14}{res}{space 2} .9915056{col 26}{space 2} .0169418{col 37}{space 1}   58.52{col 46}{space 3}0.000{col 54}{space 4} .9583003{col 67}{space 3} 1.024711
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{p 0 15 22}Instrumented:{space 2}ROLC pi_hat_F1{p_end}
{p 0 15 22}Instruments:{space 3}pi_hat_1 pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 ROLC_3 ROLC_4 pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2 pi_pc_3 pi_pc_4 longshort_spread_1 longshort_spread_2 longshort_spread_3 longshort_spread_4 logy_detrended_1 logy_detrended_2 logy_detrended_3 logy_detrended_4{p_end}
HAC VCE:{col 16}Bartlett kernel with 9 lags
HAC Lags:{col 16}Chosen by Newey-West method
WMat Lags:{col 16}Chosen by Newey-West method

{com}. 
. estat overid

{txt}{col 3}Test of overidentifying restriction:

{col 3}Hansen's J chi2({res}22{txt}) ={res} 9.07094{txt} (p = {res}0.9930{txt})

{com}. 
. matrix list e(V)
{res}
{txt}symmetric e(V)[2,2]
                ROLC  pi_hat_F1
     ROLC {res} .00021553
{txt}pi_hat_F1 {res}  .0000155  .00028702
{reset}
{com}. 
. ivreg2  pi_hat ( ROLC pi_hat_F1= pi_hat_1  pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 ROLC_3 ROLC_4 pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2  pi_pc_3 pi_pc_4 longshort_spread_1 longshort_spread_2 longshort_spread_3 longshort_spread_4 logy_detrended_1 logy_detrended_2 logy_detrended_3 logy_detrended_4) in 123/238, noconstant robust gmm2s nofooter bw(10) first ffirst
{res}
{txt}First-stage regressions
{hline 23}

First-stage regression of ROLC:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=10
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 24,    92) = {res}   39.95
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .1078186188{txt}{col 55}Centered R2   = {res}  0.6727
{txt}Total (uncentered) SS   = {res} .1078196201{txt}{col 55}Uncentered R2 = {res}  0.6727
{txt}Residual SS             = {res} .0352856753{txt}{col 55}Root MSE      = {res}  .01958

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}              ROLC{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_1 {c |}{col 20}{res}{space 2}-.3045511{col 32}{space 2} .2422142{col 43}{space 1}   -1.26{col 52}{space 3}0.212{col 60}{space 4}-.7856094{col 73}{space 3} .1765072
{txt}{space 10}pi_hat_2 {c |}{col 20}{res}{space 2}-.2155297{col 32}{space 2} .2399654{col 43}{space 1}   -0.90{col 52}{space 3}0.371{col 60}{space 4}-.6921218{col 73}{space 3} .2610624
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2} .1723211{col 32}{space 2} .1721616{col 43}{space 1}    1.00{col 52}{space 3}0.319{col 60}{space 4}-.1696066{col 73}{space 3} .5142489
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2} .1580762{col 32}{space 2} .1444681{col 43}{space 1}    1.09{col 52}{space 3}0.277{col 60}{space 4}-.1288498{col 73}{space 3} .4450023
{txt}{space 12}ROLC_1 {c |}{col 20}{res}{space 2} .2176991{col 32}{space 2} .0707044{col 43}{space 1}    3.08{col 52}{space 3}0.003{col 60}{space 4} .0772741{col 73}{space 3} .3581241
{txt}{space 12}ROLC_2 {c |}{col 20}{res}{space 2} .2410432{col 32}{space 2} .0937036{col 43}{space 1}    2.57{col 52}{space 3}0.012{col 60}{space 4} .0549397{col 73}{space 3} .4271467
{txt}{space 12}ROLC_3 {c |}{col 20}{res}{space 2} .3358304{col 32}{space 2} .0697791{col 43}{space 1}    4.81{col 52}{space 3}0.000{col 60}{space 4}  .197243{col 73}{space 3} .4744177
{txt}{space 12}ROLC_4 {c |}{col 20}{res}{space 2} .0684596{col 32}{space 2} .0771483{col 43}{space 1}    0.89{col 52}{space 3}0.377{col 60}{space 4}-.0847637{col 73}{space 3} .2216828
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2} .1291962{col 32}{space 2} .1007589{col 43}{space 1}    1.28{col 52}{space 3}0.203{col 60}{space 4}-.0709196{col 73}{space 3} .3293119
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0933385{col 32}{space 2} .0735517{col 43}{space 1}    1.27{col 52}{space 3}0.208{col 60}{space 4}-.0527416{col 73}{space 3} .2394186
{txt}{space 12}pi_w_3 {c |}{col 20}{res}{space 2} .0214074{col 32}{space 2}  .086063{col 43}{space 1}    0.25{col 52}{space 3}0.804{col 60}{space 4}-.1495212{col 73}{space 3}  .192336
{txt}{space 12}pi_w_4 {c |}{col 20}{res}{space 2} .0842039{col 32}{space 2} .0683024{col 43}{space 1}    1.23{col 52}{space 3}0.221{col 60}{space 4}-.0514505{col 73}{space 3} .2198583
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2}-.0131701{col 32}{space 2} .1115071{col 43}{space 1}   -0.12{col 52}{space 3}0.906{col 60}{space 4}-.2346328{col 73}{space 3} .2082925
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .1340616{col 32}{space 2} .1023446{col 43}{space 1}    1.31{col 52}{space 3}0.193{col 60}{space 4}-.0692036{col 73}{space 3} .3373267
{txt}{space 11}pi_pc_3 {c |}{col 20}{res}{space 2}-.0265078{col 32}{space 2} .0938661{col 43}{space 1}   -0.28{col 52}{space 3}0.778{col 60}{space 4}-.2129341{col 73}{space 3} .1599185
{txt}{space 11}pi_pc_4 {c |}{col 20}{res}{space 2} .1587471{col 32}{space 2} .1025977{col 43}{space 1}    1.55{col 52}{space 3}0.125{col 60}{space 4}-.0450207{col 73}{space 3} .3625149
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2}-.0013247{col 32}{space 2} .0040732{col 43}{space 1}   -0.33{col 52}{space 3}0.746{col 60}{space 4}-.0094146{col 73}{space 3} .0067651
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2} .0125361{col 32}{space 2} .0054674{col 43}{space 1}    2.29{col 52}{space 3}0.024{col 60}{space 4} .0016774{col 73}{space 3} .0233947
{txt}longshort_spread_3 {c |}{col 20}{res}{space 2} -.008022{col 32}{space 2} .0049058{col 43}{space 1}   -1.64{col 52}{space 3}0.105{col 60}{space 4}-.0177654{col 73}{space 3} .0017214
{txt}longshort_spread_4 {c |}{col 20}{res}{space 2} .0012905{col 32}{space 2} .0030749{col 43}{space 1}    0.42{col 52}{space 3}0.676{col 60}{space 4}-.0048165{col 73}{space 3} .0073976
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2} .3428804{col 32}{space 2} .2417299{col 43}{space 1}    1.42{col 52}{space 3}0.159{col 60}{space 4}-.1372161{col 73}{space 3} .8229769
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2}-.1927506{col 32}{space 2} .3229147{col 43}{space 1}   -0.60{col 52}{space 3}0.552{col 60}{space 4} -.834087{col 73}{space 3} .4485858
{txt}{space 2}logy_detrended_3 {c |}{col 20}{res}{space 2} .3214957{col 32}{space 2} .3213634{col 43}{space 1}    1.00{col 52}{space 3}0.320{col 60}{space 4}-.3167598{col 73}{space 3} .9597513
{txt}{space 2}logy_detrended_4 {c |}{col 20}{res}{space 2}-.3744084{col 32}{space 2} .2344594{col 43}{space 1}   -1.60{col 52}{space 3}0.114{col 60}{space 4} -.840065{col 73}{space 3} .0912482
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_1 pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 ROLC_3
{col 23}ROLC_4 pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2 pi_pc_3
{col 23}pi_pc_4 longshort_spread_1 longshort_spread_2
{col 23}longshort_spread_3 longshort_spread_4 logy_detrended_1
{col 23}logy_detrended_2 logy_detrended_3 logy_detrended_4
{hline 78}
F test of excluded instruments:
  F( 24,    92) = {res}   39.95
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 23,    92) = {res}   38.43
{txt}  Prob > F      = {res}  0.0000

{txt}First-stage regression of pi_hat_F1:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=10
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 24,    92) = {res}   70.63
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0579688024{txt}{col 55}Centered R2   = {res}  0.8598
{txt}Total (uncentered) SS   = {res} .0582406245{txt}{col 55}Uncentered R2 = {res}  0.8605
{txt}Residual SS             = {res} .0081259847{txt}{col 55}Root MSE      = {res} .009398

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}         pi_hat_F1{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_1 {c |}{col 20}{res}{space 2} .3446882{col 32}{space 2} .0865584{col 43}{space 1}    3.98{col 52}{space 3}0.000{col 60}{space 4} .1727757{col 73}{space 3} .5166008
{txt}{space 10}pi_hat_2 {c |}{col 20}{res}{space 2}  .184811{col 32}{space 2} .1115353{col 43}{space 1}    1.66{col 52}{space 3}0.101{col 60}{space 4}-.0367077{col 73}{space 3} .4063298
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2}  .346193{col 32}{space 2} .1012185{col 43}{space 1}    3.42{col 52}{space 3}0.001{col 60}{space 4} .1451644{col 73}{space 3} .5472216
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2} -.020213{col 32}{space 2} .0961516{col 43}{space 1}   -0.21{col 52}{space 3}0.834{col 60}{space 4}-.2111783{col 73}{space 3} .1707522
{txt}{space 12}ROLC_1 {c |}{col 20}{res}{space 2} .0604041{col 32}{space 2} .0434629{col 43}{space 1}    1.39{col 52}{space 3}0.168{col 60}{space 4} -.025917{col 73}{space 3} .1467252
{txt}{space 12}ROLC_2 {c |}{col 20}{res}{space 2}-.0077001{col 32}{space 2}  .037299{col 43}{space 1}   -0.21{col 52}{space 3}0.837{col 60}{space 4}-.0817792{col 73}{space 3}  .066379
{txt}{space 12}ROLC_3 {c |}{col 20}{res}{space 2} .0113996{col 32}{space 2}   .03433{col 43}{space 1}    0.33{col 52}{space 3}0.741{col 60}{space 4}-.0567826{col 73}{space 3} .0795819
{txt}{space 12}ROLC_4 {c |}{col 20}{res}{space 2}-.0292465{col 32}{space 2} .0581165{col 43}{space 1}   -0.50{col 52}{space 3}0.616{col 60}{space 4}-.1446709{col 73}{space 3}  .086178
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2} .0618832{col 32}{space 2} .0264421{col 43}{space 1}    2.34{col 52}{space 3}0.021{col 60}{space 4} .0093669{col 73}{space 3} .1143995
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0244409{col 32}{space 2} .0346273{col 43}{space 1}    0.71{col 52}{space 3}0.482{col 60}{space 4} -.044332{col 73}{space 3} .0932138
{txt}{space 12}pi_w_3 {c |}{col 20}{res}{space 2}-.0010815{col 32}{space 2} .0356207{col 43}{space 1}   -0.03{col 52}{space 3}0.976{col 60}{space 4}-.0718273{col 73}{space 3} .0696643
{txt}{space 12}pi_w_4 {c |}{col 20}{res}{space 2} .0150365{col 32}{space 2} .0338629{col 43}{space 1}    0.44{col 52}{space 3}0.658{col 60}{space 4}-.0522181{col 73}{space 3} .0822912
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2} .0611687{col 32}{space 2} .0372493{col 43}{space 1}    1.64{col 52}{space 3}0.104{col 60}{space 4}-.0128116{col 73}{space 3} .1351491
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .0681758{col 32}{space 2} .0631596{col 43}{space 1}    1.08{col 52}{space 3}0.283{col 60}{space 4}-.0572646{col 73}{space 3} .1936162
{txt}{space 11}pi_pc_3 {c |}{col 20}{res}{space 2}  .038284{col 32}{space 2}  .040953{col 43}{space 1}    0.93{col 52}{space 3}0.352{col 60}{space 4}-.0430521{col 73}{space 3} .1196202
{txt}{space 11}pi_pc_4 {c |}{col 20}{res}{space 2}-.0205826{col 32}{space 2}  .039717{col 43}{space 1}   -0.52{col 52}{space 3}0.606{col 60}{space 4}-.0994641{col 73}{space 3} .0582989
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2} .0017668{col 32}{space 2} .0031953{col 43}{space 1}    0.55{col 52}{space 3}0.582{col 60}{space 4}-.0045793{col 73}{space 3}  .008113
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2} .0015407{col 32}{space 2} .0021112{col 43}{space 1}    0.73{col 52}{space 3}0.467{col 60}{space 4}-.0026523{col 73}{space 3} .0057337
{txt}longshort_spread_3 {c |}{col 20}{res}{space 2}-.0032989{col 32}{space 2} .0029418{col 43}{space 1}   -1.12{col 52}{space 3}0.265{col 60}{space 4}-.0091416{col 73}{space 3} .0025437
{txt}longshort_spread_4 {c |}{col 20}{res}{space 2} .0027813{col 32}{space 2} .0019945{col 43}{space 1}    1.39{col 52}{space 3}0.167{col 60}{space 4}  -.00118{col 73}{space 3} .0067426
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2} .1135235{col 32}{space 2} .1629643{col 43}{space 1}    0.70{col 52}{space 3}0.488{col 60}{space 4}-.2101376{col 73}{space 3} .4371846
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2} -.036565{col 32}{space 2} .1481141{col 43}{space 1}   -0.25{col 52}{space 3}0.806{col 60}{space 4}-.3307323{col 73}{space 3} .2576023
{txt}{space 2}logy_detrended_3 {c |}{col 20}{res}{space 2} .1339688{col 32}{space 2} .1494192{col 43}{space 1}    0.90{col 52}{space 3}0.372{col 60}{space 4}-.1627906{col 73}{space 3} .4307281
{txt}{space 2}logy_detrended_4 {c |}{col 20}{res}{space 2}-.1090166{col 32}{space 2} .1008517{col 43}{space 1}   -1.08{col 52}{space 3}0.283{col 60}{space 4}-.3093167{col 73}{space 3} .0912835
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_1 pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 ROLC_3
{col 23}ROLC_4 pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2 pi_pc_3
{col 23}pi_pc_4 longshort_spread_1 longshort_spread_2
{col 23}longshort_spread_3 longshort_spread_4 logy_detrended_1
{col 23}logy_detrended_2 logy_detrended_3 logy_detrended_4
{hline 78}
F test of excluded instruments:
  F( 24,    92) = {res}   70.63
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 23,    92) = {res}   73.44
{txt}  Prob > F      = {res}  0.0000



{txt}Summary results for first-stage regressions
{hline 43}

{col 44}{help ivreg2##apstats:(Underid)}{col 65}{help ivreg2##apstats:(Weak id)}
Variable     |{col 16}{help ivreg2##apstats:F}({res}{col 17} 24{txt},{res}    92{txt})  P-val{col 37}|{col 39}{help ivreg2##apstats:AP Chi-sq}({res} 23{txt}) P-val{col 60}|{col 62}{help ivreg2##apstats:AP F}({res}{col 67} 23{txt},{res}    92{txt})
{res}ROLC        {col 14}{txt}|{col 18}{res}   39.95{col 28}  0.0000{col 37}{txt}|{col 42}{res} 1114.61{col 51}  0.0000{col 60}{txt}|{col 65}{res}   38.43
pi_hat_F1   {col 14}{txt}|{col 18}{res}   70.63{col 28}  0.0000{col 37}{txt}|{col 42}{res} 2129.68{col 51}  0.0000{col 60}{txt}|{col 65}{res}   73.44

{txt}NB: first-stage test statistics heteroskedasticity and autocorrelation-robust

Stock-Yogo weak ID test critical values for single endogenous regressor:
{res}{txt}{col 37}5% maximal IV relative bias{res}{col 67} 21.41
{txt}{col 36}10% maximal IV relative bias{res}{col 67} 11.41
{txt}{col 36}20% maximal IV relative bias{res}{col 67}  6.22
{txt}{col 36}30% maximal IV relative bias{res}{col 67}  4.41
{txt}{col 36}10% maximal IV size{res}{col 67} 69.46
{txt}{col 36}15% maximal IV size{res}{col 67} 36.37
{txt}{col 36}20% maximal IV size{res}{col 67} 25.10
{txt}{col 36}25% maximal IV size{res}{col 67} 19.41
{txt}Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

{help ivreg2##idtest:Underidentification test}
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
{res}Kleibergen-Paap rk LM statistic{txt}{col 42}Chi-sq({res}23{txt})={res}11.10  {col 61}{txt}P-val={res}0.9821

{help ivreg2##widtest:Weak identification test}
{txt}Ho: equation is weakly identified
{res}Cragg-Donald Wald F statistic{col 65}    7.74
Kleibergen-Paap Wald rk F statistic{col 65}   37.64

{txt}Stock-Yogo weak ID test critical values for K1=2 and L1=24:
{res}{txt}{col 37}5% maximal IV relative bias{res}{col 67} 20.69
{txt}{col 36}10% maximal IV relative bias{res}{col 67} 11.05
{txt}{col 36}20% maximal IV relative bias{res}{col 67}  6.06
{txt}{col 36}30% maximal IV relative bias{res}{col 67}  4.32
{txt}{col 36}10% maximal IV size{res}{col 67} 53.39
{txt}{col 36}15% maximal IV size{res}{col 67} 28.42
{txt}{col 36}20% maximal IV size{res}{col 67} 19.97
{txt}{col 36}25% maximal IV size{res}{col 67} 15.64
{txt}Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

{help ivreg2##wirobust:Weak-instrument-robust inference}
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
{res}Anderson-Rubin Wald test{txt}{col 36}F({res}24{txt},{res}92{txt})={col 49}{res} 164.02{col 61}{txt}P-val={res}0.0000
Anderson-Rubin Wald test{txt}{col 36}Chi-sq({res}24{txt})={col 49}{res}4963.52{col 61}{txt}P-val={res}0.0000
Stock-Wright LM S statistic{txt}{col 36}Chi-sq({res}24{txt})={col 49}{res}   8.94{col 61}{txt}P-val={res}0.9977

{txt}NB: Underidentification, weak identification and weak-identification-robust
    test statistics heteroskedasticity and autocorrelation-robust

Number of observations               N  = {res}       116
{txt}Number of regressors                 K  = {res}         2
{txt}Number of endogenous regressors      K1 = {res}         2
{txt}Number of instruments                L  = {res}        24
{txt}Number of excluded instruments       L1 = {res}        24

{txt}2-Step GMM estimation
{hline 21}

Estimates efficient for arbitrary heteroskedasticity and autocorrelation
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=10
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F(  2,   114) = {res} 1726.61
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0581346117{txt}{col 55}Centered R2   = {res}  0.7904
{txt}Total (uncentered) SS   = {res} .0584658598{txt}{col 55}Uncentered R2 = {res}  0.7916
{txt}Residual SS             = {res}   .01218445{txt}{col 55}Root MSE      = {res}  .01025

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 14}{c |}{col 26}    Robust
{col 1}      pi_hat{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      z{col 46}   P>|z|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 8}ROLC {c |}{col 14}{res}{space 2}-.0342342{col 26}{space 2} .0144522{col 37}{space 1}   -2.37{col 46}{space 3}0.018{col 54}{space 4}  -.06256{col 67}{space 3}-.0059084
{txt}{space 3}pi_hat_F1 {c |}{col 14}{res}{space 2} .9915056{col 26}{space 2} .0168751{col 37}{space 1}   58.76{col 46}{space 3}0.000{col 54}{space 4}  .958431{col 67}{space 3}  1.02458
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. 
. ivregress gmm  pi_hat ( ROLC pi_hat_F1= pi_hat_1  pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 pi_w_1 pi_w_2 pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2 logy_detrended_1 logy_detrended_2) in 123/238, noconstant wmatrix(hac nwest optimal)
{res}
{txt}{col 1}Instrumental variables (GMM) regression{col 56}Number of obs{col 70}= {res}    116
{txt}{col 1}{col 56}Wald chi2({res}2{txt}){col 70}={res}       .
{txt}{col 1}{col 56}Prob > chi2{col 70}= {res}      .
{txt}{col 1}{col 56}R-squared{col 70}={res}       .
{txt}{col 1}GMM weight matrix: HAC Bartlett 5     {col 56}Root MSE{col 70}= {res} .01034

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 14}{c |}{col 26}      HAC
{col 1}      pi_hat{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      z{col 46}   P>|z|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 8}ROLC {c |}{col 14}{res}{space 2}-.0213918{col 26}{space 2} .0226533{col 37}{space 1}   -0.94{col 46}{space 3}0.345{col 54}{space 4}-.0657913{col 67}{space 3} .0230078
{txt}{space 3}pi_hat_F1 {c |}{col 14}{res}{space 2} 1.003269{col 26}{space 2} .0368795{col 37}{space 1}   27.20{col 46}{space 3}0.000{col 54}{space 4} .9309868{col 67}{space 3} 1.075552
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{p 0 15 22}Instrumented:{space 2}ROLC pi_hat_F1{p_end}
{p 0 15 22}Instruments:{space 3}pi_hat_1 pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 pi_w_1 pi_w_2 pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2 logy_detrended_1 logy_detrended_2{p_end}
HAC VCE:{col 16}Bartlett kernel with 3 lags
HAC Lags:{col 16}Chosen by Newey-West method
WMat Lags:{col 16}Chosen by Newey-West method

{com}. 
. estat overid

{txt}{col 3}Test of overidentifying restriction:

{col 3}Hansen's J chi2({res}12{txt}) ={res} 8.93329{txt} (p = {res}0.7086{txt})

{com}. 
. matrix list e(V)
{res}
{txt}symmetric e(V)[2,2]
                ROLC  pi_hat_F1
     ROLC {res} .00051317
{txt}pi_hat_F1 {res} -.0001364  .00136009
{reset}
{com}. 
. ivreg2  pi_hat ( ROLC pi_hat_F1= pi_hat_1  pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 pi_w_1 pi_w_2 pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2 logy_detrended_1 logy_detrended_2) in 123/238, noconstant robust gmm2s nofooter bw(6) first ffirst
{res}
{txt}First-stage regressions
{hline 23}

First-stage regression of ROLC:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=6
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 14,   102) = {res}   30.98
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .1078186188{txt}{col 55}Centered R2   = {res}  0.5929
{txt}Total (uncentered) SS   = {res} .1078196201{txt}{col 55}Uncentered R2 = {res}  0.5929
{txt}Residual SS             = {res} .0438954821{txt}{col 55}Root MSE      = {res}  .02074

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}              ROLC{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_1 {c |}{col 20}{res}{space 2}-.3141268{col 32}{space 2}  .317149{col 43}{space 1}   -0.99{col 52}{space 3}0.324{col 60}{space 4}-.9431903{col 73}{space 3} .3149367
{txt}{space 10}pi_hat_2 {c |}{col 20}{res}{space 2}-.0497739{col 32}{space 2} .2294475{col 43}{space 1}   -0.22{col 52}{space 3}0.829{col 60}{space 4}-.5048819{col 73}{space 3} .4053341
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2} .2079592{col 32}{space 2} .2019678{col 43}{space 1}    1.03{col 52}{space 3}0.306{col 60}{space 4}-.1926428{col 73}{space 3} .6085613
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2} .1257643{col 32}{space 2} .1542627{col 43}{space 1}    0.82{col 52}{space 3}0.417{col 60}{space 4} -.180215{col 73}{space 3} .4317436
{txt}{space 12}ROLC_1 {c |}{col 20}{res}{space 2} .3327437{col 32}{space 2} .0756041{col 43}{space 1}    4.40{col 52}{space 3}0.000{col 60}{space 4} .1827833{col 73}{space 3}  .482704
{txt}{space 12}ROLC_2 {c |}{col 20}{res}{space 2} .3784753{col 32}{space 2} .0903612{col 43}{space 1}    4.19{col 52}{space 3}0.000{col 60}{space 4} .1992442{col 73}{space 3} .5577064
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2} .1368199{col 32}{space 2} .0800689{col 43}{space 1}    1.71{col 52}{space 3}0.091{col 60}{space 4}-.0219965{col 73}{space 3} .2956362
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0395583{col 32}{space 2} .0709369{col 43}{space 1}    0.56{col 52}{space 3}0.578{col 60}{space 4}-.1011447{col 73}{space 3} .1802613
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2} .0143133{col 32}{space 2} .0871789{col 43}{space 1}    0.16{col 52}{space 3}0.870{col 60}{space 4}-.1586056{col 73}{space 3} .1872322
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .1297123{col 32}{space 2} .0994836{col 43}{space 1}    1.30{col 52}{space 3}0.195{col 60}{space 4}-.0676129{col 73}{space 3} .3270374
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2} .0013423{col 32}{space 2} .0053638{col 43}{space 1}    0.25{col 52}{space 3}0.803{col 60}{space 4}-.0092967{col 73}{space 3} .0119814
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2} .0042861{col 32}{space 2} .0054718{col 43}{space 1}    0.78{col 52}{space 3}0.435{col 60}{space 4}-.0065671{col 73}{space 3} .0151393
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2} .3686636{col 32}{space 2} .3089277{col 43}{space 1}    1.19{col 52}{space 3}0.235{col 60}{space 4}-.2440931{col 73}{space 3} .9814202
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2}-.1118248{col 32}{space 2} .2965097{col 43}{space 1}   -0.38{col 52}{space 3}0.707{col 60}{space 4}-.6999503{col 73}{space 3} .4763008
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_1 pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 pi_w_1
{col 23}pi_w_2 pi_pc_1 pi_pc_2 longshort_spread_1
{col 23}longshort_spread_2 logy_detrended_1 logy_detrended_2
{hline 78}
F test of excluded instruments:
  F( 14,   102) = {res}   30.98
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 13,   102) = {res}   27.42
{txt}  Prob > F      = {res}  0.0000

{txt}First-stage regression of pi_hat_F1:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=6
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 14,   102) = {res}   29.06
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0579688024{txt}{col 55}Centered R2   = {res}  0.8504
{txt}Total (uncentered) SS   = {res} .0582406245{txt}{col 55}Uncentered R2 = {res}  0.8511
{txt}Residual SS             = {res} .0086697085{txt}{col 55}Root MSE      = {res} .009219

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}         pi_hat_F1{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_1 {c |}{col 20}{res}{space 2} .3493511{col 32}{space 2} .1144649{col 43}{space 1}    3.05{col 52}{space 3}0.003{col 60}{space 4} .1223106{col 73}{space 3} .5763916
{txt}{space 10}pi_hat_2 {c |}{col 20}{res}{space 2} .2158971{col 32}{space 2} .1055851{col 43}{space 1}    2.04{col 52}{space 3}0.043{col 60}{space 4} .0064696{col 73}{space 3} .4253246
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2} .3709702{col 32}{space 2} .0925746{col 43}{space 1}    4.01{col 52}{space 3}0.000{col 60}{space 4} .1873488{col 73}{space 3} .5545916
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2}-.0678529{col 32}{space 2} .0872354{col 43}{space 1}   -0.78{col 52}{space 3}0.438{col 60}{space 4}-.2408838{col 73}{space 3} .1051781
{txt}{space 12}ROLC_1 {c |}{col 20}{res}{space 2} .0430883{col 32}{space 2} .0320409{col 43}{space 1}    1.34{col 52}{space 3}0.182{col 60}{space 4}-.0204646{col 73}{space 3} .1066413
{txt}{space 12}ROLC_2 {c |}{col 20}{res}{space 2}-.0075564{col 32}{space 2} .0356056{col 43}{space 1}   -0.21{col 52}{space 3}0.832{col 60}{space 4}  -.07818{col 73}{space 3} .0630672
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2} .0547376{col 32}{space 2} .0334148{col 43}{space 1}    1.64{col 52}{space 3}0.104{col 60}{space 4}-.0115405{col 73}{space 3} .1210156
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0159867{col 32}{space 2} .0319862{col 43}{space 1}    0.50{col 52}{space 3}0.618{col 60}{space 4}-.0474578{col 73}{space 3} .0794313
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2} .0486453{col 32}{space 2} .0442545{col 43}{space 1}    1.10{col 52}{space 3}0.274{col 60}{space 4}-.0391332{col 73}{space 3} .1364238
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .0666748{col 32}{space 2} .0658508{col 43}{space 1}    1.01{col 52}{space 3}0.314{col 60}{space 4}-.0639399{col 73}{space 3} .1972894
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2} .0015463{col 32}{space 2} .0036735{col 43}{space 1}    0.42{col 52}{space 3}0.675{col 60}{space 4}-.0057401{col 73}{space 3} .0088328
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2} .0008941{col 32}{space 2} .0032053{col 43}{space 1}    0.28{col 52}{space 3}0.781{col 60}{space 4}-.0054635{col 73}{space 3} .0072518
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2} .0980602{col 32}{space 2} .1984307{col 43}{space 1}    0.49{col 52}{space 3}0.622{col 60}{space 4}-.2955262{col 73}{space 3} .4916466
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2} .0259045{col 32}{space 2} .1895702{col 43}{space 1}    0.14{col 52}{space 3}0.892{col 60}{space 4}-.3501071{col 73}{space 3} .4019161
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_1 pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 pi_w_1
{col 23}pi_w_2 pi_pc_1 pi_pc_2 longshort_spread_1
{col 23}longshort_spread_2 logy_detrended_1 logy_detrended_2
{hline 78}
F test of excluded instruments:
  F( 14,   102) = {res}   29.06
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 13,   102) = {res}   29.84
{txt}  Prob > F      = {res}  0.0000



{txt}Summary results for first-stage regressions
{hline 43}

{col 44}{help ivreg2##apstats:(Underid)}{col 65}{help ivreg2##apstats:(Weak id)}
Variable     |{col 16}{help ivreg2##apstats:F}({res}{col 17} 14{txt},{res}   102{txt})  P-val{col 37}|{col 39}{help ivreg2##apstats:AP Chi-sq}({res} 13{txt}) P-val{col 60}|{col 62}{help ivreg2##apstats:AP F}({res}{col 67} 13{txt},{res}   102{txt})
{res}ROLC        {col 14}{txt}|{col 18}{res}   30.98{col 28}  0.0000{col 37}{txt}|{col 42}{res}  405.45{col 51}  0.0000{col 60}{txt}|{col 65}{res}   27.42
pi_hat_F1   {col 14}{txt}|{col 18}{res}   29.06{col 28}  0.0000{col 37}{txt}|{col 42}{res}  441.23{col 51}  0.0000{col 60}{txt}|{col 65}{res}   29.84

{txt}NB: first-stage test statistics heteroskedasticity and autocorrelation-robust

Stock-Yogo weak ID test critical values for single endogenous regressor:
{res}{txt}{col 37}5% maximal IV relative bias{res}{col 67} 21.18
{txt}{col 36}10% maximal IV relative bias{res}{col 67} 11.52
{txt}{col 36}20% maximal IV relative bias{res}{col 67}  6.49
{txt}{col 36}30% maximal IV relative bias{res}{col 67}  4.71
{txt}{col 36}10% maximal IV size{res}{col 67} 45.64
{txt}{col 36}15% maximal IV size{res}{col 67} 24.42
{txt}{col 36}20% maximal IV size{res}{col 67} 17.14
{txt}{col 36}25% maximal IV size{res}{col 67} 13.41
{txt}Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

{help ivreg2##idtest:Underidentification test}
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
{res}Kleibergen-Paap rk LM statistic{txt}{col 42}Chi-sq({res}13{txt})={res}13.02  {col 61}{txt}P-val={res}0.4460

{help ivreg2##widtest:Weak identification test}
{txt}Ho: equation is weakly identified
{res}Cragg-Donald Wald F statistic{col 65}   10.44
Kleibergen-Paap Wald rk F statistic{col 65}   23.14

{txt}Stock-Yogo weak ID test critical values for K1=2 and L1=14:
{res}{txt}{col 37}5% maximal IV relative bias{res}{col 67} 19.83
{txt}{col 36}10% maximal IV relative bias{res}{col 67} 10.89
{txt}{col 36}20% maximal IV relative bias{res}{col 67}  6.20
{txt}{col 36}30% maximal IV relative bias{res}{col 67}  4.53
{txt}{col 36}10% maximal IV size{res}{col 67} 36.36
{txt}{col 36}15% maximal IV size{res}{col 67} 19.72
{txt}{col 36}20% maximal IV size{res}{col 67} 14.05
{txt}{col 36}25% maximal IV size{res}{col 67} 11.13
{txt}Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

{help ivreg2##wirobust:Weak-instrument-robust inference}
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
{res}Anderson-Rubin Wald test{txt}{col 36}F({res}14{txt},{res}102{txt})={col 49}{res} 122.67{col 61}{txt}P-val={res}0.0000
Anderson-Rubin Wald test{txt}{col 36}Chi-sq({res}14{txt})={col 49}{res}1953.03{col 61}{txt}P-val={res}0.0000
Stock-Wright LM S statistic{txt}{col 36}Chi-sq({res}14{txt})={col 49}{res}   9.91{col 61}{txt}P-val={res}0.7686

{txt}NB: Underidentification, weak identification and weak-identification-robust
    test statistics heteroskedasticity and autocorrelation-robust

Number of observations               N  = {res}       116
{txt}Number of regressors                 K  = {res}         2
{txt}Number of endogenous regressors      K1 = {res}         2
{txt}Number of instruments                L  = {res}        14
{txt}Number of excluded instruments       L1 = {res}        14

{txt}2-Step GMM estimation
{hline 21}

Estimates efficient for arbitrary heteroskedasticity and autocorrelation
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=6
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F(  2,   114) = {res}  987.06
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0581346117{txt}{col 55}Centered R2   = {res}  0.7867
{txt}Total (uncentered) SS   = {res} .0584658598{txt}{col 55}Uncentered R2 = {res}  0.7879
{txt}Residual SS             = {res} .0123995317{txt}{col 55}Root MSE      = {res}  .01034

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 14}{c |}{col 26}    Robust
{col 1}      pi_hat{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      z{col 46}   P>|z|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 8}ROLC {c |}{col 14}{res}{space 2}-.0213918{col 26}{space 2} .0180968{col 37}{space 1}   -1.18{col 46}{space 3}0.237{col 54}{space 4}-.0568608{col 67}{space 3} .0140773
{txt}{space 3}pi_hat_F1 {c |}{col 14}{res}{space 2} 1.003269{col 26}{space 2} .0223979{col 37}{space 1}   44.79{col 46}{space 3}0.000{col 54}{space 4}   .95937{col 67}{space 3} 1.047168
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. 
. ivregress gmm  pi_hat ( RULC pi_hat_1 pi_hat_F1=  pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 RULC_3 RULC_4 pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2  pi_pc_3 pi_pc_4 longshort_spread_1 longshort_spread_2 longshort_spread_3 longshort_spread_4 logy_detrended_1 logy_detrended_2 logy_detrended_3 logy_detrended_4) in 123/238, noconstant wmatrix(hac nwest optimal)
{res}
{txt}{col 1}Instrumental variables (GMM) regression{col 56}Number of obs{col 70}= {res}    116
{txt}{col 1}{col 56}Wald chi2({res}3{txt}){col 70}={res}       .
{txt}{col 1}{col 56}Prob > chi2{col 70}= {res}      .
{txt}{col 1}{col 56}R-squared{col 70}={res}       .
{txt}{col 1}GMM weight matrix: HAC Bartlett 20    {col 56}Root MSE{col 70}= {res} .00887

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 14}{c |}{col 26}      HAC
{col 1}      pi_hat{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      z{col 46}   P>|z|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 8}RULC {c |}{col 14}{res}{space 2}  .011149{col 26}{space 2} .0089603{col 37}{space 1}    1.24{col 46}{space 3}0.213{col 54}{space 4}-.0064128{col 67}{space 3} .0287108
{txt}{space 4}pi_hat_1 {c |}{col 14}{res}{space 2} .5437633{col 26}{space 2} .0370499{col 37}{space 1}   14.68{col 46}{space 3}0.000{col 54}{space 4} .4711469{col 67}{space 3} .6163797
{txt}{space 3}pi_hat_F1 {c |}{col 14}{res}{space 2} .4410014{col 26}{space 2} .0415063{col 37}{space 1}   10.62{col 46}{space 3}0.000{col 54}{space 4} .3596504{col 67}{space 3} .5223523
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{p 0 15 22}Instrumented:{space 2}RULC pi_hat_1 pi_hat_F1{p_end}
{p 0 15 22}Instruments:{space 3}pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 RULC_3 RULC_4 pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2 pi_pc_3 pi_pc_4 longshort_spread_1 longshort_spread_2 longshort_spread_3 longshort_spread_4 logy_detrended_1 logy_detrended_2 logy_detrended_3 logy_detrended_4{p_end}
HAC VCE:{col 16}Bartlett kernel with 20 lags
HAC Lags:{col 16}Chosen by Newey-West method
WMat Lags:{col 16}Chosen by Newey-West method

{com}. 
. estat overid

{txt}{col 3}Test of overidentifying restriction:

{col 3}Hansen's J chi2({res}20{txt}) ={res} 5.85664{txt} (p = {res}0.9991{txt})

{com}. 
. matrix list e(V)
{res}
{txt}symmetric e(V)[3,3]
                 RULC    pi_hat_1   pi_hat_F1
     RULC {res}  .00008029
{txt} pi_hat_1 {res}  1.234e-07   .00137269
{txt}pi_hat_F1 {res} -.00006391  -.00148706   .00172278
{reset}
{com}. 
. ivreg2  pi_hat ( RULC pi_hat_1 pi_hat_F1=  pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 RULC_3 RULC_4 pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2  pi_pc_3 pi_pc_4 longshort_spread_1 longshort_spread_2 longshort_spread_3 longshort_spread_4 logy_detrended_1 logy_detrended_2 logy_detrended_3 logy_detrended_4) in 123/238, noconstant robust gmm2s nofooter bw(21) first ffirst
{res}
{txt}First-stage regressions
{hline 23}

First-stage regression of RULC:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=21
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 23,    93) = {res}  418.15
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0502750189{txt}{col 55}Centered R2   = {res}  0.8953
{txt}Total (uncentered) SS   = {res}  .053911445{txt}{col 55}Uncentered R2 = {res}  0.9023
{txt}Residual SS             = {res} .0052651562{txt}{col 55}Root MSE      = {res} .007524

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}              RULC{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_2 {c |}{col 20}{res}{space 2}-.1802689{col 32}{space 2} .1463961{col 43}{space 1}   -1.23{col 52}{space 3}0.221{col 60}{space 4}-.4709826{col 73}{space 3} .1104448
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2} .0086264{col 32}{space 2} .0985075{col 43}{space 1}    0.09{col 52}{space 3}0.930{col 60}{space 4}-.1869899{col 73}{space 3} .2042427
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2} .2437653{col 32}{space 2} .1420786{col 43}{space 1}    1.72{col 52}{space 3}0.090{col 60}{space 4}-.0383745{col 73}{space 3} .5259052
{txt}{space 12}RULC_1 {c |}{col 20}{res}{space 2} .6865875{col 32}{space 2} .0899104{col 43}{space 1}    7.64{col 52}{space 3}0.000{col 60}{space 4} .5080433{col 73}{space 3} .8651318
{txt}{space 12}RULC_2 {c |}{col 20}{res}{space 2} .0978894{col 32}{space 2} .1513069{col 43}{space 1}    0.65{col 52}{space 3}0.519{col 60}{space 4}-.2025762{col 73}{space 3}  .398355
{txt}{space 12}RULC_3 {c |}{col 20}{res}{space 2} .3435466{col 32}{space 2} .1970052{col 43}{space 1}    1.74{col 52}{space 3}0.084{col 60}{space 4}-.0476666{col 73}{space 3} .7347598
{txt}{space 12}RULC_4 {c |}{col 20}{res}{space 2}-.2263384{col 32}{space 2} .1408099{col 43}{space 1}   -1.61{col 52}{space 3}0.111{col 60}{space 4} -.505959{col 73}{space 3} .0532822
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2} .0293201{col 32}{space 2} .0302177{col 43}{space 1}    0.97{col 52}{space 3}0.334{col 60}{space 4}-.0306864{col 73}{space 3} .0893265
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0587687{col 32}{space 2} .0485059{col 43}{space 1}    1.21{col 52}{space 3}0.229{col 60}{space 4}-.0375544{col 73}{space 3} .1550918
{txt}{space 12}pi_w_3 {c |}{col 20}{res}{space 2}-.0922003{col 32}{space 2} .0358878{col 43}{space 1}   -2.57{col 52}{space 3}0.012{col 60}{space 4}-.1634663{col 73}{space 3}-.0209343
{txt}{space 12}pi_w_4 {c |}{col 20}{res}{space 2} .0710358{col 32}{space 2} .0225297{col 43}{space 1}    3.15{col 52}{space 3}0.002{col 60}{space 4} .0262962{col 73}{space 3} .1157754
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2}-.0002104{col 32}{space 2} .0375146{col 43}{space 1}   -0.01{col 52}{space 3}0.996{col 60}{space 4}-.0747071{col 73}{space 3} .0742862
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .0370952{col 32}{space 2} .0395299{col 43}{space 1}    0.94{col 52}{space 3}0.350{col 60}{space 4}-.0414033{col 73}{space 3} .1155937
{txt}{space 11}pi_pc_3 {c |}{col 20}{res}{space 2}-.0236157{col 32}{space 2} .0318431{col 43}{space 1}   -0.74{col 52}{space 3}0.460{col 60}{space 4}-.0868499{col 73}{space 3} .0396185
{txt}{space 11}pi_pc_4 {c |}{col 20}{res}{space 2}-.0014659{col 32}{space 2} .0252814{col 43}{space 1}   -0.06{col 52}{space 3}0.954{col 60}{space 4}-.0516698{col 73}{space 3}  .048738
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2} .0029172{col 32}{space 2} .0024291{col 43}{space 1}    1.20{col 52}{space 3}0.233{col 60}{space 4}-.0019065{col 73}{space 3} .0077409
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2} -.004917{col 32}{space 2} .0022728{col 43}{space 1}   -2.16{col 52}{space 3}0.033{col 60}{space 4}-.0094304{col 73}{space 3}-.0004036
{txt}longshort_spread_3 {c |}{col 20}{res}{space 2} .0022926{col 32}{space 2} .0022237{col 43}{space 1}    1.03{col 52}{space 3}0.305{col 60}{space 4}-.0021232{col 73}{space 3} .0067085
{txt}longshort_spread_4 {c |}{col 20}{res}{space 2}-.0010406{col 32}{space 2} .0023869{col 43}{space 1}   -0.44{col 52}{space 3}0.664{col 60}{space 4}-.0057805{col 73}{space 3} .0036993
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2} .0227818{col 32}{space 2} .2024294{col 43}{space 1}    0.11{col 52}{space 3}0.911{col 60}{space 4}-.3792028{col 73}{space 3} .4247665
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2}-.0365163{col 32}{space 2} .2978857{col 43}{space 1}   -0.12{col 52}{space 3}0.903{col 60}{space 4}-.6280582{col 73}{space 3} .5550256
{txt}{space 2}logy_detrended_3 {c |}{col 20}{res}{space 2} .5072525{col 32}{space 2} .1430607{col 43}{space 1}    3.55{col 52}{space 3}0.001{col 60}{space 4} .2231622{col 73}{space 3} .7913427
{txt}{space 2}logy_detrended_4 {c |}{col 20}{res}{space 2}-.4099993{col 32}{space 2}  .140404{col 43}{space 1}   -2.92{col 52}{space 3}0.004{col 60}{space 4}-.6888139{col 73}{space 3}-.1311847
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 RULC_3 RULC_4
{col 23}pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2 pi_pc_3
{col 23}pi_pc_4 longshort_spread_1 longshort_spread_2
{col 23}longshort_spread_3 longshort_spread_4 logy_detrended_1
{col 23}logy_detrended_2 logy_detrended_3 logy_detrended_4
{hline 78}
F test of excluded instruments:
  F( 23,    93) = {res}  418.15
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 21,    93) = {res}  174.72
{txt}  Prob > F      = {res}  0.0000

{txt}First-stage regression of pi_hat_1:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=21
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 23,    93) = {res}  437.95
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0586060405{txt}{col 55}Centered R2   = {res}  0.8913
{txt}Total (uncentered) SS   = {res} .0590151024{txt}{col 55}Uncentered R2 = {res}  0.8920
{txt}Residual SS             = {res} .0063720349{txt}{col 55}Root MSE      = {res} .008277

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}          pi_hat_1{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_2 {c |}{col 20}{res}{space 2}  .251852{col 32}{space 2} .0957174{col 43}{space 1}    2.63{col 52}{space 3}0.010{col 60}{space 4} .0617762{col 73}{space 3} .4419278
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2} .2757877{col 32}{space 2}  .088421{col 43}{space 1}    3.12{col 52}{space 3}0.002{col 60}{space 4} .1002011{col 73}{space 3} .4513743
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2}  .160373{col 32}{space 2} .0669943{col 43}{space 1}    2.39{col 52}{space 3}0.019{col 60}{space 4} .0273355{col 73}{space 3} .2934105
{txt}{space 12}RULC_1 {c |}{col 20}{res}{space 2}-.0545319{col 32}{space 2} .1519676{col 43}{space 1}   -0.36{col 52}{space 3}0.721{col 60}{space 4}-.3563093{col 73}{space 3} .2472455
{txt}{space 12}RULC_2 {c |}{col 20}{res}{space 2} .2263692{col 32}{space 2} .1548928{col 43}{space 1}    1.46{col 52}{space 3}0.147{col 60}{space 4}-.0812173{col 73}{space 3} .5339558
{txt}{space 12}RULC_3 {c |}{col 20}{res}{space 2}-.1162332{col 32}{space 2} .2890563{col 43}{space 1}   -0.40{col 52}{space 3}0.689{col 60}{space 4}-.6902417{col 73}{space 3} .4577754
{txt}{space 12}RULC_4 {c |}{col 20}{res}{space 2}-.0235952{col 32}{space 2} .1806621{col 43}{space 1}   -0.13{col 52}{space 3}0.896{col 60}{space 4}-.3823543{col 73}{space 3}  .335164
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2}  .044323{col 32}{space 2} .0374507{col 43}{space 1}    1.18{col 52}{space 3}0.240{col 60}{space 4}-.0300467{col 73}{space 3} .1186927
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0175163{col 32}{space 2} .0427842{col 43}{space 1}    0.41{col 52}{space 3}0.683{col 60}{space 4}-.0674446{col 73}{space 3} .1024771
{txt}{space 12}pi_w_3 {c |}{col 20}{res}{space 2}-.0173999{col 32}{space 2} .0427256{col 43}{space 1}   -0.41{col 52}{space 3}0.685{col 60}{space 4}-.1022445{col 73}{space 3} .0674447
{txt}{space 12}pi_w_4 {c |}{col 20}{res}{space 2} .0172483{col 32}{space 2} .0275726{col 43}{space 1}    0.63{col 52}{space 3}0.533{col 60}{space 4}-.0375054{col 73}{space 3} .0720021
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2} .1760532{col 32}{space 2} .0275692{col 43}{space 1}    6.39{col 52}{space 3}0.000{col 60}{space 4} .1213062{col 73}{space 3} .2308002
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2}  .049083{col 32}{space 2} .0327378{col 43}{space 1}    1.50{col 52}{space 3}0.137{col 60}{space 4}-.0159279{col 73}{space 3} .1140938
{txt}{space 11}pi_pc_3 {c |}{col 20}{res}{space 2} .0055764{col 32}{space 2} .0232593{col 43}{space 1}    0.24{col 52}{space 3}0.811{col 60}{space 4} -.040612{col 73}{space 3} .0517648
{txt}{space 11}pi_pc_4 {c |}{col 20}{res}{space 2} .0067407{col 32}{space 2} .0393134{col 43}{space 1}    0.17{col 52}{space 3}0.864{col 60}{space 4}-.0713279{col 73}{space 3} .0848093
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2}-.0012298{col 32}{space 2} .0017788{col 43}{space 1}   -0.69{col 52}{space 3}0.491{col 60}{space 4}-.0047621{col 73}{space 3} .0023026
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2} .0012361{col 32}{space 2} .0016515{col 43}{space 1}    0.75{col 52}{space 3}0.456{col 60}{space 4}-.0020434{col 73}{space 3} .0045157
{txt}longshort_spread_3 {c |}{col 20}{res}{space 2} .0002539{col 32}{space 2} .0021949{col 43}{space 1}    0.12{col 52}{space 3}0.908{col 60}{space 4}-.0041048{col 73}{space 3} .0046125
{txt}longshort_spread_4 {c |}{col 20}{res}{space 2} .0010348{col 32}{space 2} .0021969{col 43}{space 1}    0.47{col 52}{space 3}0.639{col 60}{space 4}-.0033278{col 73}{space 3} .0053974
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2}-.1930807{col 32}{space 2} .1694967{col 43}{space 1}   -1.14{col 52}{space 3}0.258{col 60}{space 4}-.5296677{col 73}{space 3} .1435062
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2} .3833716{col 32}{space 2} .1024848{col 43}{space 1}    3.74{col 52}{space 3}0.000{col 60}{space 4}  .179857{col 73}{space 3} .5868862
{txt}{space 2}logy_detrended_3 {c |}{col 20}{res}{space 2}-.2822927{col 32}{space 2} .3928435{col 43}{space 1}   -0.72{col 52}{space 3}0.474{col 60}{space 4}-1.062402{col 73}{space 3} .4978166
{txt}{space 2}logy_detrended_4 {c |}{col 20}{res}{space 2}  .111888{col 32}{space 2} .2600993{col 43}{space 1}    0.43{col 52}{space 3}0.668{col 60}{space 4}-.4046176{col 73}{space 3} .6283936
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 RULC_3 RULC_4
{col 23}pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2 pi_pc_3
{col 23}pi_pc_4 longshort_spread_1 longshort_spread_2
{col 23}longshort_spread_3 longshort_spread_4 logy_detrended_1
{col 23}logy_detrended_2 logy_detrended_3 logy_detrended_4
{hline 78}
F test of excluded instruments:
  F( 23,    93) = {res}  437.95
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 21,    93) = {res}   30.02
{txt}  Prob > F      = {res}  0.0000

{txt}First-stage regression of pi_hat_F1:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=21
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 23,    93) = {res}  189.03
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0579688024{txt}{col 55}Centered R2   = {res}  0.8502
{txt}Total (uncentered) SS   = {res} .0582406245{txt}{col 55}Uncentered R2 = {res}  0.8509
{txt}Residual SS             = {res} .0086829595{txt}{col 55}Root MSE      = {res} .009663

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}         pi_hat_F1{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_2 {c |}{col 20}{res}{space 2} .2269039{col 32}{space 2} .1116968{col 43}{space 1}    2.03{col 52}{space 3}0.045{col 60}{space 4} .0050962{col 73}{space 3} .4487116
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2} .4176097{col 32}{space 2} .0903329{col 43}{space 1}    4.62{col 52}{space 3}0.000{col 60}{space 4} .2382264{col 73}{space 3} .5969929
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2} .0697447{col 32}{space 2} .1011728{col 43}{space 1}    0.69{col 52}{space 3}0.492{col 60}{space 4}-.1311645{col 73}{space 3} .2706539
{txt}{space 12}RULC_1 {c |}{col 20}{res}{space 2} .0863257{col 32}{space 2} .1127208{col 43}{space 1}    0.77{col 52}{space 3}0.446{col 60}{space 4}-.1375154{col 73}{space 3} .3101668
{txt}{space 12}RULC_2 {c |}{col 20}{res}{space 2}-.4669121{col 32}{space 2} .2129045{col 43}{space 1}   -2.19{col 52}{space 3}0.031{col 60}{space 4}-.8896983{col 73}{space 3}-.0441259
{txt}{space 12}RULC_3 {c |}{col 20}{res}{space 2} .3050325{col 32}{space 2} .2994208{col 43}{space 1}    1.02{col 52}{space 3}0.311{col 60}{space 4}-.2895578{col 73}{space 3} .8996228
{txt}{space 12}RULC_4 {c |}{col 20}{res}{space 2} .1037326{col 32}{space 2} .1783147{col 43}{space 1}    0.58{col 52}{space 3}0.562{col 60}{space 4}-.2503651{col 73}{space 3} .4578303
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2} .0698046{col 32}{space 2} .0292341{col 43}{space 1}    2.39{col 52}{space 3}0.019{col 60}{space 4} .0117514{col 73}{space 3} .1278578
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .1038482{col 32}{space 2} .0484532{col 43}{space 1}    2.14{col 52}{space 3}0.035{col 60}{space 4} .0076298{col 73}{space 3} .2000666
{txt}{space 12}pi_w_3 {c |}{col 20}{res}{space 2} .0118669{col 32}{space 2} .0534292{col 43}{space 1}    0.22{col 52}{space 3}0.825{col 60}{space 4}-.0942329{col 73}{space 3} .1179667
{txt}{space 12}pi_w_4 {c |}{col 20}{res}{space 2} .0060562{col 32}{space 2} .0364626{col 43}{space 1}    0.17{col 52}{space 3}0.868{col 60}{space 4}-.0663512{col 73}{space 3} .0784637
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2} .1321204{col 32}{space 2} .0491656{col 43}{space 1}    2.69{col 52}{space 3}0.009{col 60}{space 4} .0344873{col 73}{space 3} .2297535
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .1268111{col 32}{space 2}  .064055{col 43}{space 1}    1.98{col 52}{space 3}0.051{col 60}{space 4}-.0003895{col 73}{space 3} .2540117
{txt}{space 11}pi_pc_3 {c |}{col 20}{res}{space 2} .0412464{col 32}{space 2} .0330013{col 43}{space 1}    1.25{col 52}{space 3}0.214{col 60}{space 4}-.0242877{col 73}{space 3} .1067805
{txt}{space 11}pi_pc_4 {c |}{col 20}{res}{space 2}-.0318276{col 32}{space 2} .0417544{col 43}{space 1}   -0.76{col 52}{space 3}0.448{col 60}{space 4}-.1147437{col 73}{space 3} .0510884
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2} .0009807{col 32}{space 2} .0030541{col 43}{space 1}    0.32{col 52}{space 3}0.749{col 60}{space 4}-.0050842{col 73}{space 3} .0070456
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2} .0014703{col 32}{space 2} .0016497{col 43}{space 1}    0.89{col 52}{space 3}0.375{col 60}{space 4}-.0018058{col 73}{space 3} .0047463
{txt}longshort_spread_3 {c |}{col 20}{res}{space 2}-.0021505{col 32}{space 2} .0023552{col 43}{space 1}   -0.91{col 52}{space 3}0.364{col 60}{space 4}-.0068274{col 73}{space 3} .0025264
{txt}longshort_spread_4 {c |}{col 20}{res}{space 2} .0031984{col 32}{space 2}  .002062{col 43}{space 1}    1.55{col 52}{space 3}0.124{col 60}{space 4}-.0008963{col 73}{space 3} .0072932
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2} .2241752{col 32}{space 2} .1147348{col 43}{space 1}    1.95{col 52}{space 3}0.054{col 60}{space 4}-.0036654{col 73}{space 3} .4520158
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2} -.410553{col 32}{space 2} .1852917{col 43}{space 1}   -2.22{col 52}{space 3}0.029{col 60}{space 4}-.7785055{col 73}{space 3}-.0426005
{txt}{space 2}logy_detrended_3 {c |}{col 20}{res}{space 2} .4379046{col 32}{space 2} .3297127{col 43}{space 1}    1.33{col 52}{space 3}0.187{col 60}{space 4}-.2168395{col 73}{space 3} 1.092649
{txt}{space 2}logy_detrended_4 {c |}{col 20}{res}{space 2} -.101103{col 32}{space 2} .1815726{col 43}{space 1}   -0.56{col 52}{space 3}0.579{col 60}{space 4}-.4616701{col 73}{space 3} .2594642
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 RULC_3 RULC_4
{col 23}pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2 pi_pc_3
{col 23}pi_pc_4 longshort_spread_1 longshort_spread_2
{col 23}longshort_spread_3 longshort_spread_4 logy_detrended_1
{col 23}logy_detrended_2 logy_detrended_3 logy_detrended_4
{hline 78}
F test of excluded instruments:
  F( 23,    93) = {res}  189.03
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 21,    93) = {res}   14.20
{txt}  Prob > F      = {res}  0.0000



{txt}Summary results for first-stage regressions
{hline 43}

{col 44}{help ivreg2##apstats:(Underid)}{col 65}{help ivreg2##apstats:(Weak id)}
Variable     |{col 16}{help ivreg2##apstats:F}({res}{col 17} 23{txt},{res}    93{txt})  P-val{col 37}|{col 39}{help ivreg2##apstats:AP Chi-sq}({res} 21{txt}) P-val{col 60}|{col 62}{help ivreg2##apstats:AP F}({res}{col 67} 21{txt},{res}    93{txt})
{res}RULC        {col 14}{txt}|{col 18}{res}  418.15{col 28}  0.0000{col 37}{txt}|{col 42}{res} 4576.61{col 51}  0.0000{col 60}{txt}|{col 65}{res}  174.72
pi_hat_1    {col 14}{txt}|{col 18}{res}  437.95{col 28}  0.0000{col 37}{txt}|{col 42}{res}  786.31{col 51}  0.0000{col 60}{txt}|{col 65}{res}   30.02
pi_hat_F1   {col 14}{txt}|{col 18}{res}  189.03{col 28}  0.0000{col 37}{txt}|{col 42}{res}  372.03{col 51}  0.0000{col 60}{txt}|{col 65}{res}   14.20

{txt}NB: first-stage test statistics heteroskedasticity and autocorrelation-robust

Stock-Yogo weak ID test critical values for single endogenous regressor:
{res}{txt}{col 37}5% maximal IV relative bias{res}{col 67} 21.41
{txt}{col 36}10% maximal IV relative bias{res}{col 67} 11.44
{txt}{col 36}20% maximal IV relative bias{res}{col 67}  6.26
{txt}{col 36}30% maximal IV relative bias{res}{col 67}  4.46
{txt}{col 36}10% maximal IV size{res}{col 67} 64.69
{txt}{col 36}15% maximal IV size{res}{col 67} 33.97
{txt}{col 36}20% maximal IV size{res}{col 67} 23.50
{txt}{col 36}25% maximal IV size{res}{col 67} 18.20
{txt}Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

{help ivreg2##idtest:Underidentification test}
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
{res}Kleibergen-Paap rk LM statistic{txt}{col 42}Chi-sq({res}21{txt})={res}6.08   {col 61}{txt}P-val={res}0.9994

{help ivreg2##widtest:Weak identification test}
{txt}Ho: equation is weakly identified
{res}Cragg-Donald Wald F statistic{col 65}    1.31
Kleibergen-Paap Wald rk F statistic{col 65}   18.47

{txt}Stock-Yogo weak ID test critical values for K1=3 and L1=23:
{res}{txt}{col 37}5% maximal IV relative bias{res}{col 67} 19.86
{txt}{col 36}10% maximal IV relative bias{res}{col 67} 10.68
{txt}{col 36}20% maximal IV relative bias{res}{col 67}  5.92
{txt}{col 36}30% maximal IV relative bias{res}{col 67}  4.25
{txt}Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

{help ivreg2##wirobust:Weak-instrument-robust inference}
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
{res}Anderson-Rubin Wald test{txt}{col 36}F({res}23{txt},{res}93{txt})={col 49}{res} 200.46{col 61}{txt}P-val={res}0.0000
Anderson-Rubin Wald test{txt}{col 36}Chi-sq({res}23{txt})={col 49}{res}5750.97{col 61}{txt}P-val={res}0.0000
Stock-Wright LM S statistic{txt}{col 36}Chi-sq({res}23{txt})={col 49}{res}   5.72{col 61}{txt}P-val={res}0.9999

{txt}NB: Underidentification, weak identification and weak-identification-robust
    test statistics heteroskedasticity and autocorrelation-robust

Number of observations               N  = {res}       116
{txt}Number of regressors                 K  = {res}         3
{txt}Number of endogenous regressors      K1 = {res}         3
{txt}Number of instruments                L  = {res}        23
{txt}Number of excluded instruments       L1 = {res}        23

{txt}2-Step GMM estimation
{hline 21}

Estimates efficient for arbitrary heteroskedasticity and autocorrelation
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=21
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F(  3,   113) = {res} 5921.29
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0581346117{txt}{col 55}Centered R2   = {res}  0.8431
{txt}Total (uncentered) SS   = {res} .0584658598{txt}{col 55}Uncentered R2 = {res}  0.8440
{txt}Residual SS             = {res} .0091197662{txt}{col 55}Root MSE      = {res} .008867

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 14}{c |}{col 26}    Robust
{col 1}      pi_hat{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      z{col 46}   P>|z|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 8}RULC {c |}{col 14}{res}{space 2}  .011149{col 26}{space 2} .0088607{col 37}{space 1}    1.26{col 46}{space 3}0.208{col 54}{space 4}-.0062176{col 67}{space 3} .0285156
{txt}{space 4}pi_hat_1 {c |}{col 14}{res}{space 2} .5437633{col 26}{space 2} .0370209{col 37}{space 1}   14.69{col 46}{space 3}0.000{col 54}{space 4} .4712037{col 67}{space 3} .6163229
{txt}{space 3}pi_hat_F1 {c |}{col 14}{res}{space 2} .4410014{col 26}{space 2} .0414362{col 37}{space 1}   10.64{col 46}{space 3}0.000{col 54}{space 4} .3597878{col 67}{space 3} .5222149
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. 
. ivregress gmm  pi_hat ( RULC pi_hat_1 pi_hat_F1 = pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 pi_w_1 pi_w_2 pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2 logy_detrended_1 logy_detrended_2) in 123/238, noconstant wmatrix(hac nwest optimal)
{res}
{txt}{col 1}Instrumental variables (GMM) regression{col 56}Number of obs{col 70}= {res}    116
{txt}{col 1}{col 56}Wald chi2({res}3{txt}){col 70}={res}       .
{txt}{col 1}{col 56}Prob > chi2{col 70}= {res}      .
{txt}{col 1}{col 56}R-squared{col 70}={res}       .
{txt}{col 1}GMM weight matrix: HAC Bartlett 20    {col 56}Root MSE{col 70}= {res}  .0089

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 14}{c |}{col 26}      HAC
{col 1}      pi_hat{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      z{col 46}   P>|z|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 8}RULC {c |}{col 14}{res}{space 2} .0175038{col 26}{space 2} .0110221{col 37}{space 1}    1.59{col 46}{space 3}0.112{col 54}{space 4}-.0040991{col 67}{space 3} .0391067
{txt}{space 4}pi_hat_1 {c |}{col 14}{res}{space 2} .5827539{col 26}{space 2}  .050033{col 37}{space 1}   11.65{col 46}{space 3}0.000{col 54}{space 4} .4846909{col 67}{space 3} .6808169
{txt}{space 3}pi_hat_F1 {c |}{col 14}{res}{space 2}  .396386{col 26}{space 2} .0548418{col 37}{space 1}    7.23{col 46}{space 3}0.000{col 54}{space 4}  .288898{col 67}{space 3} .5038739
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{p 0 15 22}Instrumented:{space 2}RULC pi_hat_1 pi_hat_F1{p_end}
{p 0 15 22}Instruments:{space 3}pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 pi_w_1 pi_w_2 pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2 logy_detrended_1 logy_detrended_2{p_end}
HAC VCE:{col 16}Bartlett kernel with 20 lags
HAC Lags:{col 16}Chosen by Newey-West method
WMat Lags:{col 16}Chosen by Newey-West method

{com}. 
. estat overid

{txt}{col 3}Test of overidentifying restriction:

{col 3}Hansen's J chi2({res}10{txt}) ={res} 5.61944{txt} (p = {res}0.8462{txt})

{com}. 
. matrix list e(V)
{res}
{txt}symmetric e(V)[3,3]
                 RULC    pi_hat_1   pi_hat_F1
     RULC {res}  .00012149
{txt} pi_hat_1 {res} -.00005957   .00250331
{txt}pi_hat_F1 {res} -5.794e-06  -.00268529   .00300762
{reset}
{com}. 
. ivreg2  pi_hat ( RULC pi_hat_1 pi_hat_F1=  pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 pi_w_1 pi_w_2 pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2 logy_detrended_1 logy_detrended_2) in 123/238, noconstant robust gmm2s nofooter bw(21) first ffirst
{res}
{txt}First-stage regressions
{hline 23}

First-stage regression of RULC:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=21
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 13,   103) = {res}  310.76
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0502750189{txt}{col 55}Centered R2   = {res}  0.8732
{txt}Total (uncentered) SS   = {res}  .053911445{txt}{col 55}Uncentered R2 = {res}  0.8817
{txt}Residual SS             = {res} .0063754674{txt}{col 55}Root MSE      = {res} .007868

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}              RULC{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_2 {c |}{col 20}{res}{space 2}-.1474599{col 32}{space 2} .1330672{col 43}{space 1}   -1.11{col 52}{space 3}0.270{col 60}{space 4}-.4113673{col 73}{space 3} .1164476
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2}-.0081133{col 32}{space 2} .0734752{col 43}{space 1}   -0.11{col 52}{space 3}0.912{col 60}{space 4}-.1538341{col 73}{space 3} .1376075
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2}  .219512{col 32}{space 2} .1186357{col 43}{space 1}    1.85{col 52}{space 3}0.067{col 60}{space 4}-.0157739{col 73}{space 3} .4547978
{txt}{space 12}RULC_1 {c |}{col 20}{res}{space 2}  .733239{col 32}{space 2} .1054619{col 43}{space 1}    6.95{col 52}{space 3}0.000{col 60}{space 4} .5240802{col 73}{space 3} .9423978
{txt}{space 12}RULC_2 {c |}{col 20}{res}{space 2} .1624916{col 32}{space 2} .1155003{col 43}{space 1}    1.41{col 52}{space 3}0.162{col 60}{space 4}-.0665759{col 73}{space 3} .3915592
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2}-.0067686{col 32}{space 2} .0252011{col 43}{space 1}   -0.27{col 52}{space 3}0.789{col 60}{space 4}-.0567491{col 73}{space 3} .0432119
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0401019{col 32}{space 2} .0347654{col 43}{space 1}    1.15{col 52}{space 3}0.251{col 60}{space 4} -.028847{col 73}{space 3} .1090508
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2}-.0413721{col 32}{space 2} .0325909{col 43}{space 1}   -1.27{col 52}{space 3}0.207{col 60}{space 4}-.1060085{col 73}{space 3} .0232642
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .0446792{col 32}{space 2} .0330436{col 43}{space 1}    1.35{col 52}{space 3}0.179{col 60}{space 4} -.020855{col 73}{space 3} .1102134
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2} .0023743{col 32}{space 2} .0024991{col 43}{space 1}    0.95{col 52}{space 3}0.344{col 60}{space 4}-.0025821{col 73}{space 3} .0073308
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2}-.0032541{col 32}{space 2} .0023563{col 43}{space 1}   -1.38{col 52}{space 3}0.170{col 60}{space 4}-.0079272{col 73}{space 3} .0014189
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2} .1467526{col 32}{space 2} .1303946{col 43}{space 1}    1.13{col 52}{space 3}0.263{col 60}{space 4}-.1118543{col 73}{space 3} .4053595
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2}-.0263882{col 32}{space 2} .1409701{col 43}{space 1}   -0.19{col 52}{space 3}0.852{col 60}{space 4}-.3059691{col 73}{space 3} .2531928
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 pi_w_1 pi_w_2
{col 23}pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2
{col 23}logy_detrended_1 logy_detrended_2
{hline 78}
F test of excluded instruments:
  F( 13,   103) = {res}  310.76
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 11,   103) = {res}  173.92
{txt}  Prob > F      = {res}  0.0000

{txt}First-stage regression of pi_hat_1:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=21
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 13,   103) = {res}  398.79
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0586060405{txt}{col 55}Centered R2   = {res}  0.8882
{txt}Total (uncentered) SS   = {res} .0590151024{txt}{col 55}Uncentered R2 = {res}  0.8889
{txt}Residual SS             = {res} .0065537798{txt}{col 55}Root MSE      = {res} .007977

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}          pi_hat_1{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_2 {c |}{col 20}{res}{space 2} .2428905{col 32}{space 2} .0704358{col 43}{space 1}    3.45{col 52}{space 3}0.001{col 60}{space 4} .1031977{col 73}{space 3} .3825833
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2} .2846017{col 32}{space 2} .0743672{col 43}{space 1}    3.83{col 52}{space 3}0.000{col 60}{space 4} .1371118{col 73}{space 3} .4320915
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2} .1673027{col 32}{space 2} .0465351{col 43}{space 1}    3.60{col 52}{space 3}0.000{col 60}{space 4} .0750113{col 73}{space 3} .2595941
{txt}{space 12}RULC_1 {c |}{col 20}{res}{space 2}-.0437837{col 32}{space 2} .1339244{col 43}{space 1}   -0.33{col 52}{space 3}0.744{col 60}{space 4}-.3093912{col 73}{space 3} .2218238
{txt}{space 12}RULC_2 {c |}{col 20}{res}{space 2} .0620467{col 32}{space 2} .1288465{col 43}{space 1}    0.48{col 52}{space 3}0.631{col 60}{space 4}-.1934899{col 73}{space 3} .3175832
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2} .0391723{col 32}{space 2} .0303865{col 43}{space 1}    1.29{col 52}{space 3}0.200{col 60}{space 4}-.0210922{col 73}{space 3} .0994368
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0339062{col 32}{space 2}  .030481{col 43}{space 1}    1.11{col 52}{space 3}0.269{col 60}{space 4}-.0265457{col 73}{space 3}  .094358
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2} .1765796{col 32}{space 2} .0324807{col 43}{space 1}    5.44{col 52}{space 3}0.000{col 60}{space 4} .1121618{col 73}{space 3} .2409974
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .0602105{col 32}{space 2} .0342274{col 43}{space 1}    1.76{col 52}{space 3}0.082{col 60}{space 4}-.0076714{col 73}{space 3} .1280925
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2}-.0012133{col 32}{space 2} .0017874{col 43}{space 1}   -0.68{col 52}{space 3}0.499{col 60}{space 4}-.0047582{col 73}{space 3} .0023316
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2} .0021393{col 32}{space 2} .0015879{col 43}{space 1}    1.35{col 52}{space 3}0.181{col 60}{space 4}-.0010099{col 73}{space 3} .0052884
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2}-.1329376{col 32}{space 2} .1293567{col 43}{space 1}   -1.03{col 52}{space 3}0.307{col 60}{space 4}-.3894861{col 73}{space 3} .1236109
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2}  .162189{col 32}{space 2} .1387013{col 43}{space 1}    1.17{col 52}{space 3}0.245{col 60}{space 4}-.1128923{col 73}{space 3} .4372702
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 pi_w_1 pi_w_2
{col 23}pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2
{col 23}logy_detrended_1 logy_detrended_2
{hline 78}
F test of excluded instruments:
  F( 13,   103) = {res}  398.79
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 11,   103) = {res}   33.72
{txt}  Prob > F      = {res}  0.0000

{txt}First-stage regression of pi_hat_F1:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=21
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 13,   103) = {res}   89.56
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0579688024{txt}{col 55}Centered R2   = {res}  0.8361
{txt}Total (uncentered) SS   = {res} .0582406245{txt}{col 55}Uncentered R2 = {res}  0.8368
{txt}Residual SS             = {res} .0095038274{txt}{col 55}Root MSE      = {res} .009606

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}         pi_hat_F1{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_2 {c |}{col 20}{res}{space 2} .3023344{col 32}{space 2} .0953461{col 43}{space 1}    3.17{col 52}{space 3}0.002{col 60}{space 4} .1132379{col 73}{space 3}  .491431
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2} .4812066{col 32}{space 2} .0782501{col 43}{space 1}    6.15{col 52}{space 3}0.000{col 60}{space 4}  .326016{col 73}{space 3} .6363972
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2} .0109811{col 32}{space 2} .0905981{col 43}{space 1}    0.12{col 52}{space 3}0.904{col 60}{space 4}-.1686989{col 73}{space 3} .1906612
{txt}{space 12}RULC_1 {c |}{col 20}{res}{space 2} .0715405{col 32}{space 2} .1125898{col 43}{space 1}    0.64{col 52}{space 3}0.527{col 60}{space 4}-.1517547{col 73}{space 3} .2948358
{txt}{space 12}RULC_2 {c |}{col 20}{res}{space 2}-.1042327{col 32}{space 2} .1081434{col 43}{space 1}   -0.96{col 52}{space 3}0.337{col 60}{space 4}-.3187097{col 73}{space 3} .1102443
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2}  .058987{col 32}{space 2} .0276745{col 43}{space 1}    2.13{col 52}{space 3}0.035{col 60}{space 4} .0041012{col 73}{space 3} .1138727
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2}  .041965{col 32}{space 2} .0276194{col 43}{space 1}    1.52{col 52}{space 3}0.132{col 60}{space 4}-.0128116{col 73}{space 3} .0967415
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2} .1069885{col 32}{space 2} .0498869{col 43}{space 1}    2.14{col 52}{space 3}0.034{col 60}{space 4} .0080497{col 73}{space 3} .2059273
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .0932115{col 32}{space 2} .0661421{col 43}{space 1}    1.41{col 52}{space 3}0.162{col 60}{space 4}-.0379658{col 73}{space 3} .2243887
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2} .0015842{col 32}{space 2} .0028792{col 43}{space 1}    0.55{col 52}{space 3}0.583{col 60}{space 4} -.004126{col 73}{space 3} .0072944
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2} .0014865{col 32}{space 2} .0017739{col 43}{space 1}    0.84{col 52}{space 3}0.404{col 60}{space 4}-.0020315{col 73}{space 3} .0050046
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2} .1355176{col 32}{space 2} .1507194{col 43}{space 1}    0.90{col 52}{space 3}0.371{col 60}{space 4}-.1633988{col 73}{space 3}  .434434
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2} .0221836{col 32}{space 2} .1473743{col 43}{space 1}    0.15{col 52}{space 3}0.881{col 60}{space 4}-.2700986{col 73}{space 3} .3144658
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_2 pi_hat_3 pi_hat_4 RULC_1 RULC_2 pi_w_1 pi_w_2
{col 23}pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2
{col 23}logy_detrended_1 logy_detrended_2
{hline 78}
F test of excluded instruments:
  F( 13,   103) = {res}   89.56
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 11,   103) = {res}    6.43
{txt}  Prob > F      = {res}  0.0000



{txt}Summary results for first-stage regressions
{hline 43}

{col 44}{help ivreg2##apstats:(Underid)}{col 65}{help ivreg2##apstats:(Weak id)}
Variable     |{col 16}{help ivreg2##apstats:F}({res}{col 17} 13{txt},{res}   103{txt})  P-val{col 37}|{col 39}{help ivreg2##apstats:AP Chi-sq}({res} 11{txt}) P-val{col 60}|{col 62}{help ivreg2##apstats:AP F}({res}{col 67} 11{txt},{res}   103{txt})
{res}RULC        {col 14}{txt}|{col 18}{res}  310.76{col 28}  0.0000{col 37}{txt}|{col 42}{res} 2154.57{col 51}  0.0000{col 60}{txt}|{col 65}{res}  173.92
pi_hat_1    {col 14}{txt}|{col 18}{res}  398.79{col 28}  0.0000{col 37}{txt}|{col 42}{res}  417.75{col 51}  0.0000{col 60}{txt}|{col 65}{res}   33.72
pi_hat_F1   {col 14}{txt}|{col 18}{res}   89.56{col 28}  0.0000{col 37}{txt}|{col 42}{res}   79.70{col 51}  0.0000{col 60}{txt}|{col 65}{res}    6.43

{txt}NB: first-stage test statistics heteroskedasticity and autocorrelation-robust

Stock-Yogo weak ID test critical values for single endogenous regressor:
{res}{txt}{col 37}5% maximal IV relative bias{res}{col 67} 21.10
{txt}{col 36}10% maximal IV relative bias{res}{col 67} 11.51
{txt}{col 36}20% maximal IV relative bias{res}{col 67}  6.56
{txt}{col 36}30% maximal IV relative bias{res}{col 67}  4.80
{txt}{col 36}10% maximal IV size{res}{col 67} 40.90
{txt}{col 36}15% maximal IV size{res}{col 67} 22.06
{txt}{col 36}20% maximal IV size{res}{col 67} 15.56
{txt}{col 36}25% maximal IV size{res}{col 67} 12.23
{txt}Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

{help ivreg2##idtest:Underidentification test}
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
{res}Kleibergen-Paap rk LM statistic{txt}{col 42}Chi-sq({res}11{txt})={res}5.61   {col 61}{txt}P-val={res}0.8983

{help ivreg2##widtest:Weak identification test}
{txt}Ho: equation is weakly identified
{res}Cragg-Donald Wald F statistic{col 65}    1.45
Kleibergen-Paap Wald rk F statistic{col 65}    6.23

{txt}Stock-Yogo weak ID test critical values for K1=3 and L1=13:
{res}{txt}{col 37}5% maximal IV relative bias{res}{col 67} 18.17
{txt}{col 36}10% maximal IV relative bias{res}{col 67} 10.14
{txt}{col 36}20% maximal IV relative bias{res}{col 67}  5.92
{txt}{col 36}30% maximal IV relative bias{res}{col 67}  4.41
{txt}Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

{help ivreg2##wirobust:Weak-instrument-robust inference}
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
{res}Anderson-Rubin Wald test{txt}{col 36}F({res}13{txt},{res}103{txt})={col 49}{res} 243.02{col 61}{txt}P-val={res}0.0000
Anderson-Rubin Wald test{txt}{col 36}Chi-sq({res}13{txt})={col 49}{res}3557.95{col 61}{txt}P-val={res}0.0000
Stock-Wright LM S statistic{txt}{col 36}Chi-sq({res}13{txt})={col 49}{res}   5.41{col 61}{txt}P-val={res}0.9650

{txt}NB: Underidentification, weak identification and weak-identification-robust
    test statistics heteroskedasticity and autocorrelation-robust

Number of observations               N  = {res}       116
{txt}Number of regressors                 K  = {res}         3
{txt}Number of endogenous regressors      K1 = {res}         3
{txt}Number of instruments                L  = {res}        13
{txt}Number of excluded instruments       L1 = {res}        13

{txt}2-Step GMM estimation
{hline 21}

Estimates efficient for arbitrary heteroskedasticity and autocorrelation
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=21
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F(  3,   113) = {res} 4299.53
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0581346117{txt}{col 55}Centered R2   = {res}  0.8420
{txt}Total (uncentered) SS   = {res} .0584658598{txt}{col 55}Uncentered R2 = {res}  0.8429
{txt}Residual SS             = {res} .0091861019{txt}{col 55}Root MSE      = {res} .008899

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 14}{c |}{col 26}    Robust
{col 1}      pi_hat{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      z{col 46}   P>|z|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 8}RULC {c |}{col 14}{res}{space 2} .0175038{col 26}{space 2} .0109444{col 37}{space 1}    1.60{col 46}{space 3}0.110{col 54}{space 4}-.0039468{col 67}{space 3} .0389545
{txt}{space 4}pi_hat_1 {c |}{col 14}{res}{space 2} .5827539{col 26}{space 2} .0498116{col 37}{space 1}   11.70{col 46}{space 3}0.000{col 54}{space 4} .4851249{col 67}{space 3} .6803829
{txt}{space 3}pi_hat_F1 {c |}{col 14}{res}{space 2}  .396386{col 26}{space 2} .0546208{col 37}{space 1}    7.26{col 46}{space 3}0.000{col 54}{space 4} .2893312{col 67}{space 3} .5034408
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. 
. ivregress gmm  pi_hat ( ROLC pi_hat_1 pi_hat_F1=  pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 ROLC_3 ROLC_4 pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2  pi_pc_3 pi_pc_4 longshort_spread_1 longshort_spread_2 longshort_spread_3 longshort_spread_4 logy_detrended_1 logy_detrended_2 logy_detrended_3 logy_detrended_4) in 123/238, noconstant wmatrix(hac nwest optimal)
{res}
{txt}{col 1}Instrumental variables (GMM) regression{col 56}Number of obs{col 70}= {res}    116
{txt}{col 1}{col 56}Wald chi2({res}3{txt}){col 70}={res}       .
{txt}{col 1}{col 56}Prob > chi2{col 70}= {res}      .
{txt}{col 1}{col 56}R-squared{col 70}={res}       .
{txt}{col 1}GMM weight matrix: HAC Bartlett 20    {col 56}Root MSE{col 70}= {res} .00902

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 14}{c |}{col 26}      HAC
{col 1}      pi_hat{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      z{col 46}   P>|z|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 8}ROLC {c |}{col 14}{res}{space 2} .0226614{col 26}{space 2} .0102686{col 37}{space 1}    2.21{col 46}{space 3}0.027{col 54}{space 4} .0025353{col 67}{space 3} .0427875
{txt}{space 4}pi_hat_1 {c |}{col 14}{res}{space 2} .6479968{col 26}{space 2} .0570558{col 37}{space 1}   11.36{col 46}{space 3}0.000{col 54}{space 4} .5361696{col 67}{space 3}  .759824
{txt}{space 3}pi_hat_F1 {c |}{col 14}{res}{space 2} .3336367{col 26}{space 2} .0606232{col 37}{space 1}    5.50{col 46}{space 3}0.000{col 54}{space 4} .2148175{col 67}{space 3} .4524559
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{p 0 15 22}Instrumented:{space 2}ROLC pi_hat_1 pi_hat_F1{p_end}
{p 0 15 22}Instruments:{space 3}pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 ROLC_3 ROLC_4 pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2 pi_pc_3 pi_pc_4 longshort_spread_1 longshort_spread_2 longshort_spread_3 longshort_spread_4 logy_detrended_1 logy_detrended_2 logy_detrended_3 logy_detrended_4{p_end}
HAC VCE:{col 16}Bartlett kernel with 20 lags
HAC Lags:{col 16}Chosen by Newey-West method
WMat Lags:{col 16}Chosen by Newey-West method

{com}. 
. estat overid

{txt}{col 3}Test of overidentifying restriction:

{col 3}Hansen's J chi2({res}20{txt}) ={res} 6.10717{txt} (p = {res}0.9987{txt})

{com}. 
. matrix list e(V)
{res}
{txt}symmetric e(V)[3,3]
                 ROLC    pi_hat_1   pi_hat_F1
     ROLC {res}  .00010544
{txt} pi_hat_1 {res}  .00043819   .00325536
{txt}pi_hat_F1 {res} -.00045102  -.00341891   .00367517
{reset}
{com}. 
. ivreg2  pi_hat ( ROLC pi_hat_1  pi_hat_F1=  pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 ROLC_3 ROLC_4 pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2  pi_pc_3 pi_pc_4 longshort_spread_1 longshort_spread_2 longshort_spread_3 longshort_spread_4 logy_detrended_1 logy_detrended_2 logy_detrended_3 logy_detrended_4) in 123/238, noconstant robust gmm2s nofooter bw(21) first ffirst
{res}
{txt}First-stage regressions
{hline 23}

First-stage regression of ROLC:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=21
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 23,    93) = {res}  108.03
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .1078186188{txt}{col 55}Centered R2   = {res}  0.6674
{txt}Total (uncentered) SS   = {res} .1078196201{txt}{col 55}Uncentered R2 = {res}  0.6674
{txt}Residual SS             = {res}  .035859335{txt}{col 55}Root MSE      = {res}  .01964

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}              ROLC{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_2 {c |}{col 20}{res}{space 2}-.2897657{col 32}{space 2} .2803923{col 43}{space 1}   -1.03{col 52}{space 3}0.304{col 60}{space 4}-.8465692{col 73}{space 3} .2670378
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2} .0825714{col 32}{space 2}  .139195{col 43}{space 1}    0.59{col 52}{space 3}0.554{col 60}{space 4}-.1938423{col 73}{space 3} .3589852
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2} .1087262{col 32}{space 2}  .149622{col 43}{space 1}    0.73{col 52}{space 3}0.469{col 60}{space 4}-.1883933{col 73}{space 3} .4058458
{txt}{space 12}ROLC_1 {c |}{col 20}{res}{space 2} .2260402{col 32}{space 2} .0724669{col 43}{space 1}    3.12{col 52}{space 3}0.002{col 60}{space 4} .0821354{col 73}{space 3} .3699451
{txt}{space 12}ROLC_2 {c |}{col 20}{res}{space 2} .2261028{col 32}{space 2}  .084186{col 43}{space 1}    2.69{col 52}{space 3}0.009{col 60}{space 4} .0589262{col 73}{space 3} .3932794
{txt}{space 12}ROLC_3 {c |}{col 20}{res}{space 2} .3213416{col 32}{space 2} .0550708{col 43}{space 1}    5.84{col 52}{space 3}0.000{col 60}{space 4} .2119818{col 73}{space 3} .4307013
{txt}{space 12}ROLC_4 {c |}{col 20}{res}{space 2} .0865087{col 32}{space 2} .0597069{col 43}{space 1}    1.45{col 52}{space 3}0.151{col 60}{space 4}-.0320573{col 73}{space 3} .2050747
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2} .1171562{col 32}{space 2} .1010628{col 43}{space 1}    1.16{col 52}{space 3}0.249{col 60}{space 4}-.0835345{col 73}{space 3} .3178469
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0798926{col 32}{space 2} .0643094{col 43}{space 1}    1.24{col 52}{space 3}0.217{col 60}{space 4} -.047813{col 73}{space 3} .2075983
{txt}{space 12}pi_w_3 {c |}{col 20}{res}{space 2}  .030176{col 32}{space 2} .0745369{col 43}{space 1}    0.40{col 52}{space 3}0.687{col 60}{space 4}-.1178396{col 73}{space 3} .1781915
{txt}{space 12}pi_w_4 {c |}{col 20}{res}{space 2} .0774696{col 32}{space 2}  .057193{col 43}{space 1}    1.35{col 52}{space 3}0.179{col 60}{space 4}-.0361042{col 73}{space 3} .1910435
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2}-.0682189{col 32}{space 2} .1149733{col 43}{space 1}   -0.59{col 52}{space 3}0.554{col 60}{space 4} -.296533{col 73}{space 3} .1600953
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .1165871{col 32}{space 2} .0873243{col 43}{space 1}    1.34{col 52}{space 3}0.185{col 60}{space 4}-.0568217{col 73}{space 3} .2899959
{txt}{space 11}pi_pc_3 {c |}{col 20}{res}{space 2}-.0270105{col 32}{space 2} .0859219{col 43}{space 1}   -0.31{col 52}{space 3}0.754{col 60}{space 4}-.1976343{col 73}{space 3} .1436134
{txt}{space 11}pi_pc_4 {c |}{col 20}{res}{space 2} .1571293{col 32}{space 2} .0857226{col 43}{space 1}    1.83{col 52}{space 3}0.070{col 60}{space 4}-.0130988{col 73}{space 3} .3273573
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2}-.0010837{col 32}{space 2} .0037061{col 43}{space 1}   -0.29{col 52}{space 3}0.771{col 60}{space 4}-.0084431{col 73}{space 3} .0062758
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2} .0123077{col 32}{space 2} .0045353{col 43}{space 1}    2.71{col 52}{space 3}0.008{col 60}{space 4} .0033014{col 73}{space 3} .0213139
{txt}longshort_spread_3 {c |}{col 20}{res}{space 2}-.0083395{col 32}{space 2} .0040595{col 43}{space 1}   -2.05{col 52}{space 3}0.043{col 60}{space 4}-.0164008{col 73}{space 3}-.0002781
{txt}longshort_spread_4 {c |}{col 20}{res}{space 2} .0012569{col 32}{space 2} .0026661{col 43}{space 1}    0.47{col 52}{space 3}0.638{col 60}{space 4}-.0040374{col 73}{space 3} .0065513
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2} .3801932{col 32}{space 2} .2322271{col 43}{space 1}    1.64{col 52}{space 3}0.105{col 60}{space 4}-.0809638{col 73}{space 3} .8413502
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2}-.2590307{col 32}{space 2} .2697552{col 43}{space 1}   -0.96{col 52}{space 3}0.339{col 60}{space 4}-.7947111{col 73}{space 3} .2766498
{txt}{space 2}logy_detrended_3 {c |}{col 20}{res}{space 2} .3835797{col 32}{space 2} .2562968{col 43}{space 1}    1.50{col 52}{space 3}0.138{col 60}{space 4}-.1253749{col 73}{space 3} .8925344
{txt}{space 2}logy_detrended_4 {c |}{col 20}{res}{space 2}-.4133169{col 32}{space 2} .1590868{col 43}{space 1}   -2.60{col 52}{space 3}0.011{col 60}{space 4}-.7292318{col 73}{space 3} -.097402
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 ROLC_3 ROLC_4
{col 23}pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2 pi_pc_3
{col 23}pi_pc_4 longshort_spread_1 longshort_spread_2
{col 23}longshort_spread_3 longshort_spread_4 logy_detrended_1
{col 23}logy_detrended_2 logy_detrended_3 logy_detrended_4
{hline 78}
F test of excluded instruments:
  F( 23,    93) = {res}  108.03
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 21,    93) = {res}   92.78
{txt}  Prob > F      = {res}  0.0000

{txt}First-stage regression of pi_hat_1:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=21
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 23,    93) = {res}  434.65
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0586060405{txt}{col 55}Centered R2   = {res}  0.8945
{txt}Total (uncentered) SS   = {res} .0590151024{txt}{col 55}Uncentered R2 = {res}  0.8952
{txt}Residual SS             = {res} .0061849196{txt}{col 55}Root MSE      = {res} .008155

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}          pi_hat_1{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_2 {c |}{col 20}{res}{space 2} .2437557{col 32}{space 2} .0784105{col 43}{space 1}    3.11{col 52}{space 3}0.002{col 60}{space 4} .0880479{col 73}{space 3} .3994634
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2} .2946951{col 32}{space 2} .0745499{col 43}{space 1}    3.95{col 52}{space 3}0.000{col 60}{space 4} .1466539{col 73}{space 3} .4427363
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2} .1620418{col 32}{space 2} .0581745{col 43}{space 1}    2.79{col 52}{space 3}0.006{col 60}{space 4} .0465187{col 73}{space 3} .2775649
{txt}{space 12}ROLC_1 {c |}{col 20}{res}{space 2}-.0273882{col 32}{space 2} .0491013{col 43}{space 1}   -0.56{col 52}{space 3}0.578{col 60}{space 4}-.1248936{col 73}{space 3} .0701172
{txt}{space 12}ROLC_2 {c |}{col 20}{res}{space 2} .0490571{col 32}{space 2} .0248548{col 43}{space 1}    1.97{col 52}{space 3}0.051{col 60}{space 4}-.0002997{col 73}{space 3} .0984139
{txt}{space 12}ROLC_3 {c |}{col 20}{res}{space 2} .0475743{col 32}{space 2} .0472062{col 43}{space 1}    1.01{col 52}{space 3}0.316{col 60}{space 4} -.046168{col 73}{space 3} .1413165
{txt}{space 12}ROLC_4 {c |}{col 20}{res}{space 2}-.0592647{col 32}{space 2} .0380122{col 43}{space 1}   -1.56{col 52}{space 3}0.122{col 60}{space 4}-.1347494{col 73}{space 3}   .01622
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2} .0395334{col 32}{space 2} .0232488{col 43}{space 1}    1.70{col 52}{space 3}0.092{col 60}{space 4}-.0066342{col 73}{space 3}  .085701
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0441497{col 32}{space 2} .0399052{col 43}{space 1}    1.11{col 52}{space 3}0.271{col 60}{space 4}-.0350941{col 73}{space 3} .1233935
{txt}{space 12}pi_w_3 {c |}{col 20}{res}{space 2}-.0287917{col 32}{space 2} .0229929{col 43}{space 1}   -1.25{col 52}{space 3}0.214{col 60}{space 4}-.0744509{col 73}{space 3} .0168676
{txt}{space 12}pi_w_4 {c |}{col 20}{res}{space 2} .0221119{col 32}{space 2} .0220895{col 43}{space 1}    1.00{col 52}{space 3}0.319{col 60}{space 4}-.0217534{col 73}{space 3} .0659773
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2} .1807537{col 32}{space 2} .0229241{col 43}{space 1}    7.88{col 52}{space 3}0.000{col 60}{space 4} .1352309{col 73}{space 3} .2262765
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .0573778{col 32}{space 2} .0312206{col 43}{space 1}    1.84{col 52}{space 3}0.069{col 60}{space 4}-.0046202{col 73}{space 3} .1193757
{txt}{space 11}pi_pc_3 {c |}{col 20}{res}{space 2} .0016506{col 32}{space 2} .0180372{col 43}{space 1}    0.09{col 52}{space 3}0.927{col 60}{space 4}-.0341677{col 73}{space 3} .0374689
{txt}{space 11}pi_pc_4 {c |}{col 20}{res}{space 2} .0053122{col 32}{space 2} .0319995{col 43}{space 1}    0.17{col 52}{space 3}0.869{col 60}{space 4}-.0582325{col 73}{space 3}  .068857
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2}-.0007916{col 32}{space 2} .0015664{col 43}{space 1}   -0.51{col 52}{space 3}0.614{col 60}{space 4}-.0039021{col 73}{space 3} .0023188
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2} .0007501{col 32}{space 2} .0015904{col 43}{space 1}    0.47{col 52}{space 3}0.638{col 60}{space 4}-.0024082{col 73}{space 3} .0039083
{txt}longshort_spread_3 {c |}{col 20}{res}{space 2} .0010424{col 32}{space 2} .0026185{col 43}{space 1}    0.40{col 52}{space 3}0.691{col 60}{space 4}-.0041576{col 73}{space 3} .0062423
{txt}longshort_spread_4 {c |}{col 20}{res}{space 2} .0001103{col 32}{space 2} .0021987{col 43}{space 1}    0.05{col 52}{space 3}0.960{col 60}{space 4}-.0042558{col 73}{space 3} .0044765
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2}-.1225174{col 32}{space 2} .1450306{col 43}{space 1}   -0.84{col 52}{space 3}0.400{col 60}{space 4}-.4105195{col 73}{space 3} .1654846
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2} .2176319{col 32}{space 2}  .131945{col 43}{space 1}    1.65{col 52}{space 3}0.102{col 60}{space 4}-.0443846{col 73}{space 3} .4796485
{txt}{space 2}logy_detrended_3 {c |}{col 20}{res}{space 2}-.2038542{col 32}{space 2} .1605924{col 43}{space 1}   -1.27{col 52}{space 3}0.207{col 60}{space 4}-.5227588{col 73}{space 3} .1150504
{txt}{space 2}logy_detrended_4 {c |}{col 20}{res}{space 2} .1277571{col 32}{space 2} .1262638{col 43}{space 1}    1.01{col 52}{space 3}0.314{col 60}{space 4}-.1229777{col 73}{space 3} .3784919
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 ROLC_3 ROLC_4
{col 23}pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2 pi_pc_3
{col 23}pi_pc_4 longshort_spread_1 longshort_spread_2
{col 23}longshort_spread_3 longshort_spread_4 logy_detrended_1
{col 23}logy_detrended_2 logy_detrended_3 logy_detrended_4
{hline 78}
F test of excluded instruments:
  F( 23,    93) = {res}  434.65
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 21,    93) = {res}   16.34
{txt}  Prob > F      = {res}  0.0000

{txt}First-stage regression of pi_hat_F1:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=21
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 23,    93) = {res}  206.71
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0579688024{txt}{col 55}Centered R2   = {res}  0.8471
{txt}Total (uncentered) SS   = {res} .0582406245{txt}{col 55}Uncentered R2 = {res}  0.8479
{txt}Residual SS             = {res} .0088608149{txt}{col 55}Root MSE      = {res} .009761

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}         pi_hat_F1{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_2 {c |}{col 20}{res}{space 2} .2688308{col 32}{space 2} .1038839{col 43}{space 1}    2.59{col 52}{space 3}0.011{col 60}{space 4} .0625379{col 73}{space 3} .4751236
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2}  .447771{col 32}{space 2} .0834507{col 43}{space 1}    5.37{col 52}{space 3}0.000{col 60}{space 4} .2820545{col 73}{space 3} .6134874
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2} .0356408{col 32}{space 2} .1034005{col 43}{space 1}    0.34{col 52}{space 3}0.731{col 60}{space 4}-.1696921{col 73}{space 3} .2409738
{txt}{space 12}ROLC_1 {c |}{col 20}{res}{space 2} .0509637{col 32}{space 2} .0385618{col 43}{space 1}    1.32{col 52}{space 3}0.190{col 60}{space 4}-.0256124{col 73}{space 3} .1275398
{txt}{space 12}ROLC_2 {c |}{col 20}{res}{space 2} .0092093{col 32}{space 2} .0343419{col 43}{space 1}    0.27{col 52}{space 3}0.789{col 60}{space 4} -.058987{col 73}{space 3} .0774056
{txt}{space 12}ROLC_3 {c |}{col 20}{res}{space 2} .0277979{col 32}{space 2} .0429174{col 43}{space 1}    0.65{col 52}{space 3}0.519{col 60}{space 4}-.0574275{col 73}{space 3} .1130234
{txt}{space 12}ROLC_4 {c |}{col 20}{res}{space 2}-.0496743{col 32}{space 2} .0581533{col 43}{space 1}   -0.85{col 52}{space 3}0.395{col 60}{space 4}-.1651552{col 73}{space 3} .0658065
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2} .0755099{col 32}{space 2} .0203496{col 43}{space 1}    3.71{col 52}{space 3}0.000{col 60}{space 4} .0350995{col 73}{space 3} .1159203
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0396587{col 32}{space 2} .0275217{col 43}{space 1}    1.44{col 52}{space 3}0.153{col 60}{space 4}-.0149939{col 73}{space 3} .0943114
{txt}{space 12}pi_w_3 {c |}{col 20}{res}{space 2}-.0110057{col 32}{space 2}  .037099{col 43}{space 1}   -0.30{col 52}{space 3}0.767{col 60}{space 4}-.0846769{col 73}{space 3} .0626656
{txt}{space 12}pi_w_4 {c |}{col 20}{res}{space 2} .0226583{col 32}{space 2} .0361461{col 43}{space 1}    0.63{col 52}{space 3}0.532{col 60}{space 4}-.0491208{col 73}{space 3} .0944373
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2} .1234724{col 32}{space 2} .0387555{col 43}{space 1}    3.19{col 52}{space 3}0.002{col 60}{space 4} .0465116{col 73}{space 3} .2004332
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .0879532{col 32}{space 2} .0641475{col 43}{space 1}    1.37{col 52}{space 3}0.174{col 60}{space 4} -.039431{col 73}{space 3} .2153375
{txt}{space 11}pi_pc_3 {c |}{col 20}{res}{space 2}  .038853{col 32}{space 2}  .040547{col 43}{space 1}    0.96{col 52}{space 3}0.340{col 60}{space 4}-.0416654{col 73}{space 3} .1193713
{txt}{space 11}pi_pc_4 {c |}{col 20}{res}{space 2}-.0187515{col 32}{space 2} .0425682{col 43}{space 1}   -0.44{col 52}{space 3}0.661{col 60}{space 4}-.1032836{col 73}{space 3} .0657805
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2}  .001494{col 32}{space 2} .0027278{col 43}{space 1}    0.55{col 52}{space 3}0.585{col 60}{space 4}-.0039229{col 73}{space 3} .0069109
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2} .0017993{col 32}{space 2} .0016479{col 43}{space 1}    1.09{col 52}{space 3}0.278{col 60}{space 4}-.0014732{col 73}{space 3} .0050717
{txt}longshort_spread_3 {c |}{col 20}{res}{space 2}-.0029396{col 32}{space 2} .0020346{col 43}{space 1}   -1.44{col 52}{space 3}0.152{col 60}{space 4}-.0069799{col 73}{space 3} .0011006
{txt}longshort_spread_4 {c |}{col 20}{res}{space 2} .0028193{col 32}{space 2} .0018798{col 43}{space 1}    1.50{col 52}{space 3}0.137{col 60}{space 4}-.0009136{col 73}{space 3} .0065521
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2} .0712932{col 32}{space 2} .1470256{col 43}{space 1}    0.48{col 52}{space 3}0.629{col 60}{space 4}-.2206705{col 73}{space 3} .3632569
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2} .0384502{col 32}{space 2} .1190726{col 43}{space 1}    0.32{col 52}{space 3}0.747{col 60}{space 4}-.1980044{col 73}{space 3} .2749047
{txt}{space 2}logy_detrended_3 {c |}{col 20}{res}{space 2} .0637026{col 32}{space 2} .1384828{col 43}{space 1}    0.46{col 52}{space 3}0.647{col 60}{space 4}-.2112967{col 73}{space 3}  .338702
{txt}{space 2}logy_detrended_4 {c |}{col 20}{res}{space 2}-.0649802{col 32}{space 2} .1050986{col 43}{space 1}   -0.62{col 52}{space 3}0.538{col 60}{space 4}-.2736852{col 73}{space 3} .1437247
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 ROLC_3 ROLC_4
{col 23}pi_w_1 pi_w_2 pi_w_3 pi_w_4 pi_pc_1 pi_pc_2 pi_pc_3
{col 23}pi_pc_4 longshort_spread_1 longshort_spread_2
{col 23}longshort_spread_3 longshort_spread_4 logy_detrended_1
{col 23}logy_detrended_2 logy_detrended_3 logy_detrended_4
{hline 78}
F test of excluded instruments:
  F( 23,    93) = {res}  206.71
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 21,    93) = {res}    5.72
{txt}  Prob > F      = {res}  0.0000



{txt}Summary results for first-stage regressions
{hline 43}

{col 44}{help ivreg2##apstats:(Underid)}{col 65}{help ivreg2##apstats:(Weak id)}
Variable     |{col 16}{help ivreg2##apstats:F}({res}{col 17} 23{txt},{res}    93{txt})  P-val{col 37}|{col 39}{help ivreg2##apstats:AP Chi-sq}({res} 21{txt}) P-val{col 60}|{col 62}{help ivreg2##apstats:AP F}({res}{col 67} 21{txt},{res}    93{txt})
{res}ROLC        {col 14}{txt}|{col 18}{res}  108.03{col 28}  0.0000{col 37}{txt}|{col 42}{res} 2430.35{col 51}  0.0000{col 60}{txt}|{col 65}{res}   92.78
pi_hat_1    {col 14}{txt}|{col 18}{res}  434.65{col 28}  0.0000{col 37}{txt}|{col 42}{res}  427.91{col 51}  0.0000{col 60}{txt}|{col 65}{res}   16.34
pi_hat_F1   {col 14}{txt}|{col 18}{res}  206.71{col 28}  0.0000{col 37}{txt}|{col 42}{res}  149.79{col 51}  0.0000{col 60}{txt}|{col 65}{res}    5.72

{txt}NB: first-stage test statistics heteroskedasticity and autocorrelation-robust

Stock-Yogo weak ID test critical values for single endogenous regressor:
{res}{txt}{col 37}5% maximal IV relative bias{res}{col 67} 21.41
{txt}{col 36}10% maximal IV relative bias{res}{col 67} 11.44
{txt}{col 36}20% maximal IV relative bias{res}{col 67}  6.26
{txt}{col 36}30% maximal IV relative bias{res}{col 67}  4.46
{txt}{col 36}10% maximal IV size{res}{col 67} 64.69
{txt}{col 36}15% maximal IV size{res}{col 67} 33.97
{txt}{col 36}20% maximal IV size{res}{col 67} 23.50
{txt}{col 36}25% maximal IV size{res}{col 67} 18.20
{txt}Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

{help ivreg2##idtest:Underidentification test}
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
{res}Kleibergen-Paap rk LM statistic{txt}{col 42}Chi-sq({res}21{txt})={res}6.13   {col 61}{txt}P-val={res}0.9993

{help ivreg2##widtest:Weak identification test}
{txt}Ho: equation is weakly identified
{res}Cragg-Donald Wald F statistic{col 65}    0.76
Kleibergen-Paap Wald rk F statistic{col 65}    4.73

{txt}Stock-Yogo weak ID test critical values for K1=3 and L1=23:
{res}{txt}{col 37}5% maximal IV relative bias{res}{col 67} 19.86
{txt}{col 36}10% maximal IV relative bias{res}{col 67} 10.68
{txt}{col 36}20% maximal IV relative bias{res}{col 67}  5.92
{txt}{col 36}30% maximal IV relative bias{res}{col 67}  4.25
{txt}Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

{help ivreg2##wirobust:Weak-instrument-robust inference}
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
{res}Anderson-Rubin Wald test{txt}{col 36}F({res}23{txt},{res}93{txt})={col 49}{res} 184.93{col 61}{txt}P-val={res}0.0000
Anderson-Rubin Wald test{txt}{col 36}Chi-sq({res}23{txt})={col 49}{res}5305.31{col 61}{txt}P-val={res}0.0000
Stock-Wright LM S statistic{txt}{col 36}Chi-sq({res}23{txt})={col 49}{res}   5.63{col 61}{txt}P-val={res}0.9999

{txt}NB: Underidentification, weak identification and weak-identification-robust
    test statistics heteroskedasticity and autocorrelation-robust

Number of observations               N  = {res}       116
{txt}Number of regressors                 K  = {res}         3
{txt}Number of endogenous regressors      K1 = {res}         3
{txt}Number of instruments                L  = {res}        23
{txt}Number of excluded instruments       L1 = {res}        23

{txt}2-Step GMM estimation
{hline 21}

Estimates efficient for arbitrary heteroskedasticity and autocorrelation
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=21
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F(  3,   113) = {res} 4181.88
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0581346117{txt}{col 55}Centered R2   = {res}  0.8375
{txt}Total (uncentered) SS   = {res} .0584658598{txt}{col 55}Uncentered R2 = {res}  0.8385
{txt}Residual SS             = {res} .0094439681{txt}{col 55}Root MSE      = {res} .009023

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 14}{c |}{col 26}    Robust
{col 1}      pi_hat{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      z{col 46}   P>|z|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 8}ROLC {c |}{col 14}{res}{space 2} .0226614{col 26}{space 2} .0104787{col 37}{space 1}    2.16{col 46}{space 3}0.031{col 54}{space 4} .0021235{col 67}{space 3} .0431993
{txt}{space 4}pi_hat_1 {c |}{col 14}{res}{space 2} .6479968{col 26}{space 2} .0572801{col 37}{space 1}   11.31{col 46}{space 3}0.000{col 54}{space 4} .5357299{col 67}{space 3} .7602637
{txt}{space 3}pi_hat_F1 {c |}{col 14}{res}{space 2} .3336367{col 26}{space 2} .0608565{col 37}{space 1}    5.48{col 46}{space 3}0.000{col 54}{space 4} .2143602{col 67}{space 3} .4529132
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. 
. ivregress gmm  pi_hat ( ROLC pi_hat_1 pi_hat_F1= pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 pi_w_1 pi_w_2 pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2 logy_detrended_1 logy_detrended_2) in 123/238, noconstant wmatrix(hac nwest optimal)
{res}
{txt}{col 1}Instrumental variables (GMM) regression{col 56}Number of obs{col 70}= {res}    116
{txt}{col 1}{col 56}Wald chi2({res}3{txt}){col 70}={res}       .
{txt}{col 1}{col 56}Prob > chi2{col 70}= {res}      .
{txt}{col 1}{col 56}R-squared{col 70}={res}       .
{txt}{col 1}GMM weight matrix: HAC Bartlett 20    {col 56}Root MSE{col 70}= {res} .00933

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 14}{c |}{col 26}      HAC
{col 1}      pi_hat{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      z{col 46}   P>|z|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 8}ROLC {c |}{col 14}{res}{space 2} .0424147{col 26}{space 2} .0172032{col 37}{space 1}    2.47{col 46}{space 3}0.014{col 54}{space 4} .0086971{col 67}{space 3} .0761323
{txt}{space 4}pi_hat_1 {c |}{col 14}{res}{space 2} .7571371{col 26}{space 2} .0792646{col 37}{space 1}    9.55{col 46}{space 3}0.000{col 54}{space 4} .6017814{col 67}{space 3} .9124928
{txt}{space 3}pi_hat_F1 {c |}{col 14}{res}{space 2} .2219461{col 26}{space 2} .0824859{col 37}{space 1}    2.69{col 46}{space 3}0.007{col 54}{space 4} .0602767{col 67}{space 3} .3836156
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{p 0 15 22}Instrumented:{space 2}ROLC pi_hat_1 pi_hat_F1{p_end}
{p 0 15 22}Instruments:{space 3}pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 pi_w_1 pi_w_2 pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2 logy_detrended_1 logy_detrended_2{p_end}
HAC VCE:{col 16}Bartlett kernel with 20 lags
HAC Lags:{col 16}Chosen by Newey-West method
WMat Lags:{col 16}Chosen by Newey-West method

{com}. 
. estat overid

{txt}{col 3}Test of overidentifying restriction:

{col 3}Hansen's J chi2({res}10{txt}) ={res} 5.79734{txt} (p = {res}0.8320{txt})

{com}. 
. matrix list e(V)
{res}
{txt}symmetric e(V)[3,3]
                 ROLC    pi_hat_1   pi_hat_F1
     ROLC {res}  .00029595
{txt} pi_hat_1 {res}  .00111372   .00628287
{txt}pi_hat_F1 {res}  -.0011099  -.00647466   .00680393
{reset}
{com}. 
. ivreg2  pi_hat ( ROLC pi_hat_1 pi_hat_F1=  pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 pi_w_1 pi_w_2 pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2 logy_detrended_1 logy_detrended_2) in 123/238, noconstant robust gmm2s nofooter bw(21) first ffirst
{res}
{txt}First-stage regressions
{hline 23}

First-stage regression of ROLC:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=21
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 13,   103) = {res}   62.19
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .1078186188{txt}{col 55}Centered R2   = {res}  0.5870
{txt}Total (uncentered) SS   = {res} .1078196201{txt}{col 55}Uncentered R2 = {res}  0.5870
{txt}Residual SS             = {res} .0445318653{txt}{col 55}Root MSE      = {res}  .02079

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}              ROLC{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_2 {c |}{col 20}{res}{space 2}-.1242986{col 32}{space 2} .2478799{col 43}{space 1}   -0.50{col 52}{space 3}0.617{col 60}{space 4}-.6159099{col 73}{space 3} .3673126
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2} .1155661{col 32}{space 2} .1411322{col 43}{space 1}    0.82{col 52}{space 3}0.415{col 60}{space 4}-.1643363{col 73}{space 3} .3954685
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2} .0713519{col 32}{space 2} .1236229{col 43}{space 1}    0.58{col 52}{space 3}0.565{col 60}{space 4}-.1738249{col 73}{space 3} .3165287
{txt}{space 12}ROLC_1 {c |}{col 20}{res}{space 2}  .342272{col 32}{space 2} .0813406{col 43}{space 1}    4.21{col 52}{space 3}0.000{col 60}{space 4}  .180952{col 73}{space 3}  .503592
{txt}{space 12}ROLC_2 {c |}{col 20}{res}{space 2} .3622506{col 32}{space 2}  .082366{col 43}{space 1}    4.40{col 52}{space 3}0.000{col 60}{space 4}  .198897{col 73}{space 3} .5256042
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2} .1237538{col 32}{space 2} .0639529{col 43}{space 1}    1.94{col 52}{space 3}0.056{col 60}{space 4}-.0030816{col 73}{space 3} .2505892
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0281265{col 32}{space 2} .0584242{col 43}{space 1}    0.48{col 52}{space 3}0.631{col 60}{space 4}-.0877442{col 73}{space 3} .1439972
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2}-.0400169{col 32}{space 2} .0705728{col 43}{space 1}   -0.57{col 52}{space 3}0.572{col 60}{space 4}-.1799813{col 73}{space 3} .0999475
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .1104852{col 32}{space 2} .0804382{col 43}{space 1}    1.37{col 52}{space 3}0.173{col 60}{space 4} -.049045{col 73}{space 3} .2700155
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2} .0017215{col 32}{space 2} .0051957{col 43}{space 1}    0.33{col 52}{space 3}0.741{col 60}{space 4}-.0085829{col 73}{space 3}  .012026
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2} .0036525{col 32}{space 2}  .005393{col 43}{space 1}    0.68{col 52}{space 3}0.500{col 60}{space 4}-.0070432{col 73}{space 3} .0143482
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2}  .398118{col 32}{space 2}  .342329{col 43}{space 1}    1.16{col 52}{space 3}0.248{col 60}{space 4}-.2808109{col 73}{space 3} 1.077047
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2}-.1440859{col 32}{space 2} .3477523{col 43}{space 1}   -0.41{col 52}{space 3}0.679{col 60}{space 4}-.8337705{col 73}{space 3} .5455988
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 pi_w_1 pi_w_2
{col 23}pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2
{col 23}logy_detrended_1 logy_detrended_2
{hline 78}
F test of excluded instruments:
  F( 13,   103) = {res}   62.19
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 11,   103) = {res}   27.33
{txt}  Prob > F      = {res}  0.0000

{txt}First-stage regression of pi_hat_1:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=21
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 13,   103) = {res}  314.55
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0586060405{txt}{col 55}Centered R2   = {res}  0.8900
{txt}Total (uncentered) SS   = {res} .0590151024{txt}{col 55}Uncentered R2 = {res}  0.8907
{txt}Residual SS             = {res} .0064492438{txt}{col 55}Root MSE      = {res} .007913

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}          pi_hat_1{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_2 {c |}{col 20}{res}{space 2}  .237244{col 32}{space 2} .0674579{col 43}{space 1}    3.52{col 52}{space 3}0.001{col 60}{space 4} .1034571{col 73}{space 3} .3710309
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2} .2941268{col 32}{space 2} .0678324{col 43}{space 1}    4.34{col 52}{space 3}0.000{col 60}{space 4} .1595972{col 73}{space 3} .4286565
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2} .1732179{col 32}{space 2} .0402847{col 43}{space 1}    4.30{col 52}{space 3}0.000{col 60}{space 4} .0933227{col 73}{space 3} .2531131
{txt}{space 12}ROLC_1 {c |}{col 20}{res}{space 2}-.0303327{col 32}{space 2} .0345595{col 43}{space 1}   -0.88{col 52}{space 3}0.382{col 60}{space 4}-.0988734{col 73}{space 3}  .038208
{txt}{space 12}ROLC_2 {c |}{col 20}{res}{space 2} .0516503{col 32}{space 2} .0158943{col 43}{space 1}    3.25{col 52}{space 3}0.002{col 60}{space 4} .0201277{col 73}{space 3} .0831728
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2} .0415949{col 32}{space 2} .0246268{col 43}{space 1}    1.69{col 52}{space 3}0.094{col 60}{space 4}-.0072466{col 73}{space 3} .0904363
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0363923{col 32}{space 2} .0315924{col 43}{space 1}    1.15{col 52}{space 3}0.252{col 60}{space 4}-.0262639{col 73}{space 3} .0990484
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2} .1729565{col 32}{space 2} .0310018{col 43}{space 1}    5.58{col 52}{space 3}0.000{col 60}{space 4} .1114718{col 73}{space 3} .2344412
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .0612079{col 32}{space 2} .0341497{col 43}{space 1}    1.79{col 52}{space 3}0.076{col 60}{space 4}  -.00652{col 73}{space 3} .1289359
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2}-.0012071{col 32}{space 2}  .001627{col 43}{space 1}   -0.74{col 52}{space 3}0.460{col 60}{space 4}-.0044339{col 73}{space 3} .0020197
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2} .0020172{col 32}{space 2} .0014523{col 43}{space 1}    1.39{col 52}{space 3}0.168{col 60}{space 4}-.0008632{col 73}{space 3} .0048975
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2} -.093766{col 32}{space 2} .1238627{col 43}{space 1}   -0.76{col 52}{space 3}0.451{col 60}{space 4}-.3394183{col 73}{space 3} .1518864
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2} .1027008{col 32}{space 2}  .128854{col 43}{space 1}    0.80{col 52}{space 3}0.427{col 60}{space 4}-.1528507{col 73}{space 3} .3582523
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 pi_w_1 pi_w_2
{col 23}pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2
{col 23}logy_detrended_1 logy_detrended_2
{hline 78}
F test of excluded instruments:
  F( 13,   103) = {res}  314.55
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 11,   103) = {res}   18.23
{txt}  Prob > F      = {res}  0.0000

{txt}First-stage regression of pi_hat_F1:

OLS estimation
{hline 14}

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=21
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F( 13,   103) = {res}   97.05
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0579688024{txt}{col 55}Centered R2   = {res}  0.8369
{txt}Total (uncentered) SS   = {res} .0582406245{txt}{col 55}Uncentered R2 = {res}  0.8376
{txt}Residual SS             = {res}  .009456814{txt}{col 55}Root MSE      = {res} .009582

{txt}{hline 19}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 20}{c |}{col 32}    Robust
{col 1}         pi_hat_F1{col 20}{c |}      Coef.{col 32}   Std. Err.{col 44}      t{col 52}   P>|t|{col 60}     [95% Con{col 73}f. Interval]
{hline 19}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 10}pi_hat_2 {c |}{col 20}{res}{space 2} .2987786{col 32}{space 2} .0910499{col 43}{space 1}    3.28{col 52}{space 3}0.001{col 60}{space 4} .1182026{col 73}{space 3} .4793545
{txt}{space 10}pi_hat_3 {c |}{col 20}{res}{space 2} .4737237{col 32}{space 2} .0769754{col 43}{space 1}    6.15{col 52}{space 3}0.000{col 60}{space 4} .3210611{col 73}{space 3} .6263864
{txt}{space 10}pi_hat_4 {c |}{col 20}{res}{space 2} -.007339{col 32}{space 2} .0904135{col 43}{space 1}   -0.08{col 52}{space 3}0.935{col 60}{space 4}-.1866529{col 73}{space 3} .1719749
{txt}{space 12}ROLC_1 {c |}{col 20}{res}{space 2} .0324916{col 32}{space 2}  .040203{col 43}{space 1}    0.81{col 52}{space 3}0.421{col 60}{space 4}-.0472416{col 73}{space 3} .1122247
{txt}{space 12}ROLC_2 {c |}{col 20}{res}{space 2} .0104876{col 32}{space 2} .0416106{col 43}{space 1}    0.25{col 52}{space 3}0.802{col 60}{space 4}-.0720371{col 73}{space 3} .0930124
{txt}{space 12}pi_w_1 {c |}{col 20}{res}{space 2} .0692688{col 32}{space 2} .0268603{col 43}{space 1}    2.58{col 52}{space 3}0.011{col 60}{space 4} .0159977{col 73}{space 3} .1225399
{txt}{space 12}pi_w_2 {c |}{col 20}{res}{space 2} .0287004{col 32}{space 2} .0211876{col 43}{space 1}    1.35{col 52}{space 3}0.179{col 60}{space 4}-.0133201{col 73}{space 3} .0707209
{txt}{space 11}pi_pc_1 {c |}{col 20}{res}{space 2} .1090678{col 32}{space 2} .0432483{col 43}{space 1}    2.52{col 52}{space 3}0.013{col 60}{space 4}  .023295{col 73}{space 3} .1948406
{txt}{space 11}pi_pc_2 {c |}{col 20}{res}{space 2} .0880578{col 32}{space 2}  .063255{col 43}{space 1}    1.39{col 52}{space 3}0.167{col 60}{space 4}-.0373936{col 73}{space 3} .2135092
{txt}longshort_spread_1 {c |}{col 20}{res}{space 2} .0011246{col 32}{space 2} .0027675{col 43}{space 1}    0.41{col 52}{space 3}0.685{col 60}{space 4}-.0043641{col 73}{space 3} .0066134
{txt}longshort_spread_2 {c |}{col 20}{res}{space 2} .0015988{col 32}{space 2} .0020998{col 43}{space 1}    0.76{col 52}{space 3}0.448{col 60}{space 4}-.0025655{col 73}{space 3} .0057632
{txt}{space 2}logy_detrended_1 {c |}{col 20}{res}{space 2}  .065303{col 32}{space 2} .1510316{col 43}{space 1}    0.43{col 52}{space 3}0.666{col 60}{space 4}-.2342325{col 73}{space 3} .3648385
{txt}{space 2}logy_detrended_2 {c |}{col 20}{res}{space 2} .0617831{col 32}{space 2} .1392603{col 43}{space 1}    0.44{col 52}{space 3}0.658{col 60}{space 4}-.2144068{col 73}{space 3} .3379731
{txt}{hline 19}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
Included instruments:{col 23}pi_hat_2 pi_hat_3 pi_hat_4 ROLC_1 ROLC_2 pi_w_1 pi_w_2
{col 23}pi_pc_1 pi_pc_2 longshort_spread_1 longshort_spread_2
{col 23}logy_detrended_1 logy_detrended_2
{hline 78}
F test of excluded instruments:
  F( 13,   103) = {res}   97.05
{txt}  Prob > F      = {res}  0.0000
{help ivreg2##apstats:Angrist-Pischke multivariate F test of excluded instruments:}
{txt}  F( 11,   103) = {res}    6.08
{txt}  Prob > F      = {res}  0.0000



{txt}Summary results for first-stage regressions
{hline 43}

{col 44}{help ivreg2##apstats:(Underid)}{col 65}{help ivreg2##apstats:(Weak id)}
Variable     |{col 16}{help ivreg2##apstats:F}({res}{col 17} 13{txt},{res}   103{txt})  P-val{col 37}|{col 39}{help ivreg2##apstats:AP Chi-sq}({res} 11{txt}) P-val{col 60}|{col 62}{help ivreg2##apstats:AP F}({res}{col 67} 11{txt},{res}   103{txt})
{res}ROLC        {col 14}{txt}|{col 18}{res}   62.19{col 28}  0.0000{col 37}{txt}|{col 42}{res}  338.55{col 51}  0.0000{col 60}{txt}|{col 65}{res}   27.33
pi_hat_1    {col 14}{txt}|{col 18}{res}  314.55{col 28}  0.0000{col 37}{txt}|{col 42}{res}  225.82{col 51}  0.0000{col 60}{txt}|{col 65}{res}   18.23
pi_hat_F1   {col 14}{txt}|{col 18}{res}   97.05{col 28}  0.0000{col 37}{txt}|{col 42}{res}   75.27{col 51}  0.0000{col 60}{txt}|{col 65}{res}    6.08

{txt}NB: first-stage test statistics heteroskedasticity and autocorrelation-robust

Stock-Yogo weak ID test critical values for single endogenous regressor:
{res}{txt}{col 37}5% maximal IV relative bias{res}{col 67} 21.10
{txt}{col 36}10% maximal IV relative bias{res}{col 67} 11.51
{txt}{col 36}20% maximal IV relative bias{res}{col 67}  6.56
{txt}{col 36}30% maximal IV relative bias{res}{col 67}  4.80
{txt}{col 36}10% maximal IV size{res}{col 67} 40.90
{txt}{col 36}15% maximal IV size{res}{col 67} 22.06
{txt}{col 36}20% maximal IV size{res}{col 67} 15.56
{txt}{col 36}25% maximal IV size{res}{col 67} 12.23
{txt}Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

{help ivreg2##idtest:Underidentification test}
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
{res}Kleibergen-Paap rk LM statistic{txt}{col 42}Chi-sq({res}11{txt})={res}5.78   {col 61}{txt}P-val={res}0.8874

{help ivreg2##widtest:Weak identification test}
{txt}Ho: equation is weakly identified
{res}Cragg-Donald Wald F statistic{col 65}    0.98
Kleibergen-Paap Wald rk F statistic{col 65}    3.45

{txt}Stock-Yogo weak ID test critical values for K1=3 and L1=13:
{res}{txt}{col 37}5% maximal IV relative bias{res}{col 67} 18.17
{txt}{col 36}10% maximal IV relative bias{res}{col 67} 10.14
{txt}{col 36}20% maximal IV relative bias{res}{col 67}  5.92
{txt}{col 36}30% maximal IV relative bias{res}{col 67}  4.41
{txt}Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

{help ivreg2##wirobust:Weak-instrument-robust inference}
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
{res}Anderson-Rubin Wald test{txt}{col 36}F({res}13{txt},{res}103{txt})={col 49}{res} 184.17{col 61}{txt}P-val={res}0.0000
Anderson-Rubin Wald test{txt}{col 36}Chi-sq({res}13{txt})={col 49}{res}2696.42{col 61}{txt}P-val={res}0.0000
Stock-Wright LM S statistic{txt}{col 36}Chi-sq({res}13{txt})={col 49}{res}   5.17{col 61}{txt}P-val={res}0.9714

{txt}NB: Underidentification, weak identification and weak-identification-robust
    test statistics heteroskedasticity and autocorrelation-robust

Number of observations               N  = {res}       116
{txt}Number of regressors                 K  = {res}         3
{txt}Number of endogenous regressors      K1 = {res}         3
{txt}Number of instruments                L  = {res}        13
{txt}Number of excluded instruments       L1 = {res}        13

{txt}2-Step GMM estimation
{hline 21}

Estimates efficient for arbitrary heteroskedasticity and autocorrelation
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=21
  time variable (t):  {res}date

{txt}{col 55}Number of obs = {res}     116
{txt}{col 55}F(  3,   113) = {res} 3020.23
{txt}{col 55}Prob > F      = {res}  0.0000
{txt}Total (centered) SS     = {res} .0581346117{txt}{col 55}Centered R2   = {res}  0.8262
{txt}Total (uncentered) SS   = {res} .0584658598{txt}{col 55}Uncentered R2 = {res}  0.8272
{txt}Residual SS             = {res} .0101053866{txt}{col 55}Root MSE      = {res} .009334

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 14}{c |}{col 26}    Robust
{col 1}      pi_hat{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      z{col 46}   P>|z|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 8}ROLC {c |}{col 14}{res}{space 2} .0424147{col 26}{space 2} .0176202{col 37}{space 1}    2.41{col 46}{space 3}0.016{col 54}{space 4} .0078797{col 67}{space 3} .0769496
{txt}{space 4}pi_hat_1 {c |}{col 14}{res}{space 2} .7571371{col 26}{space 2} .0798057{col 37}{space 1}    9.49{col 46}{space 3}0.000{col 54}{space 4} .6007207{col 67}{space 3} .9135535
{txt}{space 3}pi_hat_F1 {c |}{col 14}{res}{space 2} .2219461{col 26}{space 2} .0831629{col 37}{space 1}    2.67{col 46}{space 3}0.008{col 54}{space 4} .0589498{col 67}{space 3} .3849424
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. 
. log close
      {txt}name:  {res}<unnamed>
       {txt}log:  {res}\\isad.isadroot.ex.ac.uk\uoe\user\Submitted New Keynesian Model with Overtime Labor\Referee reports RESTAT\reports 2nd round\Files for RESTAT\NKPC_gmm.smcl
  {txt}log type:  {res}smcl
 {txt}closed on:  {res}19 May 2012, 11:51:14
{txt}{.-}
{smcl}
{txt}{sf}{ul off}